non-commercial does not mean private use. private use means private use. replace with personal where necessary.
It is indeed an interesting question. I could not find a clear answer in a short time. The internet failed me.
The problem is, that the usual licences that invoke nc are intentional ambigous worded. Intent is important here, and the mere fact that money exchanges hands, does not impact this very much. You could sell a nc work at self cost, and since you do not make a profit, it is non commercial by definition. You could not sell a nc work but make advertisment for your business with it, and the intent would be profit by usage of the nc works.
Soo ... it's complicated.
Pay what you want, starting at 0 and with no buyable premium tiers sure sounds like non commercial. But if the pwyw model works and you are a business and the irs comes knocking, it will be hard to explain, that your commercial success is based on "donations".
Till better information comes up, it will be best to look for specific use cases of the assetts in question. While it is not legally possible to claim a certain license and just modify it arbitrarily, when the license giver says on their page, they allow or do not allow pwyw, you sure know what the license giver wanted to do.
We are talking about assets. No one is using assets in a personal scenario. (Maybe for internal testing, but that is a fringe scenario no one cars about, if it does not leave your own computer anyways). So the use case of that assett being used in a donation ware game should have been discussed by the license holder. Hopefully.