You generalize this without mentioning that there are LLMs which do not just use random 'dogshit'.

Also what does a normal human do? It looks around how to move one random piece and it uses a very small dictionary / set of basic rules to move it. I do not remember me learning to count every piece and its options by looking up that rulebook. I learned to 'see' how i can move one type of chess piece.

If a LLM uses only these piece moves on a mathematical level, it would do the same thing as i do.

And yes there is also absolutly the option for an LLM to learn some kind of meta game.