You are making a distinction that does not exist, between “generated” and “contributed”.
No, you are trying to make them the same. Generated is a subset of contributed. Things that are generated are always also contributed. But not the other way round. You can contribute without generating. Equating them is a formal fallacy.
And the ai disclosure specifically asks about generated content. Not about contributions or assistance.
Inspiration is not contribution.
It is. You seem to make a distinction by agency or some other arbitrary criteria. Agency is not necessary. Relevance is. Without that specific inspiration, the work would be a different work.
So what about creating a character by ai? The characters traits, background story and so on.
The idea of the character is obviously ai generated. But does it fit the question for content produced by? If you copy things word by word, it would fit the text category. If you only use general behaviour and create your own interpretation of that character, no. But it would fit a contributed/inspired by classification.
What if you used an ai to give you a plot summary of a book. But you would write the book yourself? Is that AI content?
Interestingly enough, searching for this question tells me, that this is supposed to be "ai assisted" instead of "ai generated". And the irony is, that Itch specifically asks for "ai generated", but a year later mapped the ai-generated tag to something called ai-assisted. Much to the confusion of players and developers alike.
Assisted is much too vague to be of use as a label. And about the true intent, I can only recommend reading this thread again, especially the answers from leafo, how certain things are to be regarded.
If you learn coding by asking ai and pester it about your coding problems, the game you create would be ai assisted. But it only contains ai code, if you actually put generated code into it. That's what I read from here https://itch.io/post/11423405