I also was talking about the desktop application. That is a chromium browser that handles updates and installation and has some helper apps in the background, like that butler. In theory. It does not work properly for all games.
There is a faq about the app, that says this https://itch.io/docs/app/faq#will-the-app-replace-the-website
We want the app to compliment the website, not replace it.
So if there where mechanics to make the app mandatory for a game, this would be strange.
After cross reading this again, https://itch.io/docs/api/overview , there might actually be the option to have an app that will not work properly without the itch launcher. The use case they imply is for online games and account verification to your game servers.
I just never encountered a game here with mandatory itch app usage. That is why I am curious.
Unless there is full integration ready to use for such a feature, I advise against reinventing the wheel. I assume you are single dev, so you should concentrate on your strengths and this should be in game development, not necessarily administrative tool creation. You also lose all the players that cannot or will not install the itch app.