Copyright requires the subject matter to have a modicum of human creativity. Nintendo's games absolutely qualify, they have people designing the games and the artwork.

"LLM output doesn't qualify for copyright protection" is an oversimplification. You aren't automatically disqualified from copyright protection if you've touched an LLM. It's just that copyright protections only apply to human creativity. You can qualify even when you use LLMs if you were humanly involved creatively with the output to a sufficient degree.