Maybe chess.com players play in a specific way, and there are lot of transcriptions of such games that these LLMs have ingested when they ingested the internet?

I don't know why it worked in this specific case, but based on earlier examples it is more likely that these kind of games were more prevalent in its dataset it was trained on than it being able to play chess in general. It still wasn't perfect, so even these games weren't rigid enough for it to reliably perform valid moves.

Yes, they remember patterns, and then applies logic to make a valid move. ChatGPT remembers patterns, but didn't apply any logic to make valid moves. There is a difference there.

ChatGPT does the pattern matching part, but not the logical part.

We have evidence right here that patterns of moves leads to 1400. To me this is evidence that 1400 level play is very rigid and mostly relies on defined openings and strategies, making it easy for an LLM to find similar games and win using standard continuations.

Just like grammar the patterns are too hard for humans to see and encode, but LLMs can encode pretty complex patterns. Domains that are easy to encode as grammars will be really easy for LLMs to solve, and the further from a grammar the harder for it.