Why do we care about this? Chess AI have long been solved problems and LLMs are just an overly brute forced approach. They will never become very efficient chess players.
The correct solution is to have a conventional chess AI as a tool and use the LLM as a front end for humanized output. A software engineer who proposes just doing it all via raw LLM should be fired.
It's a proxy for generalized reasoning.
The point isn't that LLMs are the best AI architecture for chess.