It is only enforced for assets. Unless you lie about the gen ai nature of things and claim you made it yourself, I do not think this will be a problem.
For games, the question is, how or if players will use or not use the new infos. There are catalogues of items where you would have check boxes to select which attributes the items you will see can have. Itch only has one such check box that I know of, and that is the adult content checkbox.
The rest is just tags. And those stack up to an url. However that works under the hood. In comparison, on Steam you have several account settings and when browsing games you do have check boxes. But they also have a limited pool of tags and so on. So you could check boxes for pvp, languages, some tags, the os, controller support and so on. Adding a filter to that layout to filter the 4 gen ai categories would be trivial in concept.
But on Itch with the tags, the only tag currently is no-ai and that is a catch it all. (Yeah, there are 5 positive tags, but I somehow suspect, the negative tag(s) will be used much more often).
Oh, and objectivly telling if something is gen ai or not is simple. Did you make it with a prompt of a llm gen ai system and optionally modified it afterwards? If yes, then it is "ai".
That is why all the coders are very concerned, because asking a gen ai system to spit out some code snippet and integrating it in your code is business as usual, but would qualify the whole game as "ai" under that no-ai tag.