This is so wildly incorrect I don't even know where to start.
For one, as you said yourself, they were just programmed to compute the probability of the next token. They were not programmed to play chess, chess games just happened to be in the training data.
For another, there is no formal definition of "understand", and it is therefore impossible to tell whether or not they "understand".
(But my claim was that one need to understand something to write poem about it. And the LLM can write poem about it)
For one, as you said yourself, they were just programmed to compute the probability of the next token. They were not programmed to play chess, chess games just happened to be in the training data.
For another, there is no formal definition of "understand", and it is therefore impossible to tell whether or not they "understand". (But my claim was that one need to understand something to write poem about it. And the LLM can write poem about it)