Just to point out, LLMs are genAI. Lots of code editors provide code suggestions similar to autocorrect/text suggestions using AI. Strictly I doubt any game is made without AI. Not to say it can't be deliberately avoided, but given the lack of opposition to GPT and LLMs I don't see it being considered for avoidance in the same way as art.
So Awards with constraints on "any AI usage in development" probably disqualifies most modern games.