This seems like an artifact due to the original purpose of the LLM. It was trained on human language, where the context of how a sentence arrives to a specific

This seems like an artifact due to the original purpose of the LLM. It was trained on human language, where the context of how a sentence arrives to a specific word is extremely important. All this says is that LLM do not know there is symmetry in chess that can be exploited to lower the search space. Which is a fair assumption, since there is not the same symmetry in human language.