It has no idea about the quality of it's data. "Act like x" prompts are no substitute for actual reasoning and deterministic computation which clearly chess requires.
If some mental model says that LLMs should be bad at chess, then it fails to explain why we have LLMs playing strong chess. If another mental model says the inverse, then it fails to explain why so many of these large models fail spectacularly at chess.
Clearly, there's more going on here.
Here's an experiment: give an LLM a balanced middle game board position and ask it "play a new move that a creative grandmaster has discovered, never before played in chess and explain the tactics and strategy behind it". Repeat many times. Now analyse each move in an engine and look at the distribution of moves and responses. Hypothesis: It is going to come up with a bunch of moves all over the ratings map with some sound and some fallacious arguments.
I really don't think there's anything too mysterious going on here. It just synthesizes existing knowledge and gives answers that includes bit hits, big misses and everything in between. Creators chip away at the edges to change that distribution but the fundamental workings don't change.