Can be forced through inference with CoT type of stuff. Spend tokens at each stage to draw the board for example, then spend tokens restating the rules of the game, then spend token restating the heuristics like piece value, and then spend tokens doing a minmax n-ply search.
Wildly inefficient? Probably. Could maybe generate some python to make more efficient? Maybe, yeah.
Essentially user would have to teach gpt to play chess, or training would fine tune chess towards these CoT, fine tuning, etc...
Do these models actually think about a board? Chess engines do, as much as we can say that any machine thinks. But do LLMs?