It could be that the model that does chess well just happens to have the right 'connectome' purely by accident of how the various back-propagations worked out to land on various local maxima (model weights) during training. It might even be (probably is) a non-verbal connectome that's just purely logic rules, having nothing to do with language at all, but a semantic space pattern that got landed on accidentally, which can solve this class of problem.
Reminds me of how Daniel Tammet just visually "sees" answers to math problems in his mind without even knowing how they appear. It's like he sees a virtual screen with a representation akin to numbers (the answer) just sitting there to be read out from his visual cortex. He's not 'working out' the solutions. They're just handed to him purely by some connectome effects going on in the background.