That's simple logic. Quoting you again:

> Machines are good at applying rules, so when they fail to apply rules correctly, it means they have incorrect, incomplete, or totally absent models.

If this line of reasoning applies to machines, but LLMs aren't machines, how can you derive any of these claims?

"A implies B" may be right, but you must first demonstrate A before reaching conclusion B..

> I think we are discussing whether LLMs can emulate chess playing machines

That is incorrect. We're discussing whether LLMs can play chess. Unless you think that human players also emulate chess playing machines?