Definitely the case. That being said, I think it would be hard, at least in the immediate future, to translate the concept of difficulty to a universal LLM for a bespoke/specific game. I assume most game AIs are tuned by hand to feel fair for a given difficulty level...but if you just give an LLM some new game, explain the rules and what resources/abilities it has available to it, you're stuck with adding some addendum to the tune of "and you're meant to represent an entity of 'medium' difficulty." For very well established games, it might have a sense of how given actions might fall into a skill-level hierarchy, but not for anything new.

Fine tuned LLMs though with actual experience with the game, maybe?