Not a lawyer, but, uh... contract law, actually, by violating a perpetual license to "access the content and to use, reproduce, distribute, display and perform such content as permitted through the functionality of the Service." That's from the itch.io Terms of Service, by the way, since you didn't read the rest of the thread. Though to be fair calling them thieves is wrong, that's a different thing and legally speaking the distinction is important.
When you have a license, you have rights to do what the license says you can do, and violating those is actually a breach of contract, despite what a lot of people who do not understand what a license is on the internet repeatedly say. I'm not going to explain the significance of that because I'm not a lawyer, but it is generally grounds for civil or possibly even criminal proceedings. In this case, it would be a material breach (since the ability to access the content is interrupted- requiring the user to download the content before a certain date is not sufficient for stating that you have the ability to access the content) and anticipatory breach (since the content hasn't been made inaccessible yet) but that will become an actual breach if the installer becomes unavailable.
Now, the bad news is that this is probably not going to end up really helping anyone get a fix. Breach of contract rarely results in any significant punitive damages unless there was a larger criminal action involved (like intentional fraud) and that's unlikely to be the case here, and it's almost certainly not worth the legal costs since you are not guaranteed to get legal costs paid even for a successful suit. The game is $9.99, so it's rolling the dice to hopefully not get crushed by Netflix lawyers who will almost certainly be paid more than your lawyers, and if they pad out the proceedings which big corporate lawyers are prone to do, well...) so this is going to "work" for Netflix or whoever decided it was a good idea.
The only way to really get any redress for users would be if itch.io took legal action against the removal of the game, but that seems unlikely to happen (though they could actually probably win damages beyond base value of goods and services rendered, since allowing a publisher to violate their Terms of Service erodes confidence in the platform). Though, hypothetically, I don't think the itch.io ToS shields Oxenfree's developer/publisher/whoever made the decision, as a third party to the contract, from a class action lawsuit, but that's something an actual lawyer would need to review, not me, especially since the arbitration waiver clause is very legalese heavy and potentially very broad.
Responding to the following response in an edit because the thread was locked:
Actually, breaching contract is exactly what's happening here. Let me talk about the points here and try to explain it as best I can as someone who is not a lawyer. I think part of the confusion here is the difference between criminal law and civil law. Technically, there is no crime being committed here, but this would probably be a material breach of contract (more on that later, but I'm already writing far more than is reasonable for an internet forum).
1. Perpetual licenses are perpetual, and itch.io offers a perpetual license to users that survives termination of the agreement by the publisher. Don't know what else to say about it. Now, a lot of contracts have clauses that allow for termination or revocation, but itch.io's contract actually does not (even Good Old "You Own Your" Games reserves the right to terminate your access to licenses for material breaches of contract) but in what may have been an oversight, I don't think itch.io even has that- it's a very consumer friendly terms of service, and while they do have grounds to ban your account, they don't have specific ways to terminate the license.
Of course, the consumer friendliness depends, to some extent, on whether the contract is enforced, and that's where the problem here comes in- whoever is revoking access is breaching the contract, but it's unlikely to go to court because of the way binding arbitration clauses work, unless itch.io decides to sue Netflix for this since they might actually have large enough damages to make it worth it if they win. While I would be encouraged by that decision as an itch.io user, it probably isn't a good financial or strategic decision though, since it's probably harder for them to win on someone else's rights being infringed.
Anyway, I'm not a lawyer so I can't explain the nuances of legalese confidently, but here's an article related to perpetual licenses: https://www.legalsifter.com/blog/contract-concepts-giving-a-contract-a-perpetual....
To sum it up, though, contracts (like the Terms of Service, which are a contract- https://www.iubenda.com/en/help/43147-are-terms-of-service-legally-binding - "Since they are a contract, terms and conditions are legally binding to every extent.") can be terminated or modified, but in this case the publisher does not have the rights to do so per the contract they agreed to- nothing gives them the right to terminate access by users to the product, and no clause in the agreement allows them to interfere with a license agreement.
2. Downgrading/changing products in development is a different case, and often times projects that have been modified substantially offer refunds or other relief to customers. Those who do not may run the risk of running afoul of advertising regulations, especially if they published a product with one description and delivered another. While not all developers do this, not all developers are lawyers, nor is it right when developers do this.
There is a "good faith" argument to be made when a project is intended to deliver a project and fails, but that may still result in liability- if you pay a contractor to do work on your house, and they can't complete the project, they may still be taken to court to recover damages. You'll notice that crowdfunding projects and early access software terms often include specific protections for developers in this case. Any Kickstarter reminds you that delivery of products and refunds are not guaranteed.
However, no such disclaimer was provided here. Even in the case where there is something like a server shutting down (see Concord for a good recent example) companies may issue refunds to avoid lawsuits for breach of contract. Breach of contract is not a criminal offense in and of itself, and usually civil suits for breach of contract tend to be limited to actual damages, so refunding a product basically protects a company in case of a material breach of contract most of the time. There are more complicated legal situations that don't apply here, but that starts to get into legalese I'm not qualified to explain.
It's also probably why this decision is being made by the party responsible- most of the affected users have access to Oxenfree through a bundle so the material damages are negligible in most cases since any lawyer worth their salt would argue that in a bundle of thousands of items no one item is worth the full cost of the bundle. Even if they lost that they would almost certainly be capped on material damages at $9.99 for the list price of the game, perhaps with any applicable taxes or fees the user paid (like the situation people who directly bought the game on itch.io are in). Even direct purchases are unlikely to be "worth" suing over. The binding arbitration clause probably protects Netflix in this case, so a class action is unlikely.
It's not that there's any unique reason why Netflix can actually defend this decision- they would probably lose in court if someone was able to bring a legal team of similar caliber to their own to the table and force them to follow the Terms of Service to the letter. It's just that taking them to court is a losing battle for anyone impacted unless you get a judge to award legal fees as part of the damages, which is not guaranteed in the US even if you went on to win the case, and fighting Netflix's legal team for pennies (or even the $9.99 list price) means the reward is not worth the risk. I'm not a lawyer, so I can't realistically factor in the odds of that- you can sometimes claim legal fees as damages, and you could probably make the argument that this is an abuse of the binding arbitration clause, but whether a judge would grant that is beyond my ability to reasonably guess at.
Even just filing a lawsuit in most jurisdictions costs more than that, and if your case is dismissed for any technical reason (which Netflix's lawyers would look for before anything else) you would be stuck with the cost of the case. Realistically, they could just settle and pay $9.99 or so to anyone who threatened to file a suit and that's the best anyone could get, but even hiring a lawyer to send a letter would likely cost more than it's worth.
Anyway, to get back on topic, contract law (in the US, this is governed by the Uniform Commercial Code) requires notice for updating or changing a contract, which is why whenever a service updates their terms (like Steam updating their Steam Subscriber Agreement on the 24th) they have to give you notice of the update.
This is probably why an email was sent to people who own Oxenfree on itch.io (and why there was a follow up email for people who owned it through a bundle, because initially they were not notified). However, this doesn't necessarily mean that it's valid- changing a contract requires a means to do so, and in most contracts the ways a contract can be modified are included in the contract. I don't believe that applies here, though I'm not a lawyer and there may be something I'm missing. It looks like how someone might modify a contract, but I don't think they actually have the ability to do so per the itch.io Terms of Service.
The only grounds for changing the contract I see in the itch.io Terms of Service is reserved for itch.io. The email sent to users is dressed up like how someone might update a terms of service agreement for a platform, but it's not using any actual mechanism to do so. There would be ways to make the removal of the game binding, such as by Netflix offering a key on another platform but saying "By accepting this key, you waive your rights to the product through your purchase on itch.io" (since that would be entering into a new contract that releases Netflix from their obligations to this one) but that doesn't seem to be the case here.
There are cases where a contract can be modified in other ways (https://callagylaw.com/rules-for-altering-contract-terms/ has a better breakdown than I can do) and a lawyer for Netflix would probably argue that they are still satisfying the contract by allowing users to download and retain the software and providing sufficient notice by sending out these emails, but that's a kind of loophole dependent legal argument that really hopes the court doesn't side with the consumer.
3. It's been cited in this forum thread several times, but the itch.io Terms of Service. Specifically https://itch.io/docs/legal/terms#4-publisher-content where publishers grant "To Users, a non-exclusive, perpetual license to access the content and to use, reproduce, distribute, display and perform such content as permitted through the functionality of the Service. Users shall retain a license to this content even after the content is removed from the Service."
While there is room in the preceding paragraph for publishers to remove their content from itch.io, that does not necessarily eliminate their obligation to users for availability of content or their granted license to users. While lawyers could probably fight a long battle over that last sentence that would make all of this look like child's play, it probably means the license as described in the preceding sentence, which specifically includes reproduction through the Service, which would be violated when the ability to download the content is removed.
As I've mentioned before contract law in the US is governed under the Uniform Commercial Code. I'm not going to dig through for a specific paragraph of the UCC to cite directly because I'm not a lawyer, but I've already provided some citations above that talk about contract law (based on the UCC) that explain why it applies and I'd recommend you read those instead of listening to me ramble more than I already have.
I hope this clears things up, I know it's a wall of text but there's a reason court documents aren't short.