I've not noticed this happening if you give it the FEN each move. The alternative is just blindfold chess and very few humans can do that for long.
Nothing is forcing the LLM to play 'blind'. If it's smart, it should be able to create its own representation of the chess board and update it with every move, just like a human would. Any chess engine that's sensitive to how the moves are formatted is clearly not very capable.
The LLM would only be playing 'blindfolded' if you somehow forbade it from making notes (as you effectively do by literally blindfolding a human, given how limited human working memory is). But you are not doing that. The LLM is free to keep track of the game state via whatever means it chooses.
None of this is about superhuman ability. Any human who understands a given chess notation can convert it to a visual representation of a chess board and then use that representation to choose their next move, with their usual level of performance.
> I just think this isn't a very good thing by which to evaluate LLM capabilities
I don’t think any single task is a good way to evaluate LLM capabilities, but I don’t see why chess is worse than a lot of other tasks. (Of course it is of no practical consequence whether LLMs can play chess, so if you are just making that point, then yes, I agree.)
> If there's no argument you'll accept
It’s a little unfair to suggest that I wouldn’t accept any argument whatever for your position just because I haven’t been convinced by your very brief comments so far. I could equally well say the same thing to you!