The experiment could be a little better by using a more descriptive form of notation than PGN. PGN notation's strength is the shorthand properties of it, because it is used by humans while playing the game. That is far from being a strength as LLM training data. ML algorithms, and LLMs are trained better by feeding them more descriptive and accurate data, and verbosity is not a problem at all. There is the FEN notation in which in every move the entire board is encoded.
One could easily imagine many different ways to describe a game, like encoding vertical and horizontal lines, listing what exact squares each piece is covering, what color squares, which of the pieces are able to move, and in each move generate one whole page of the board situation.
I call this spatial navigation, in which the LLM learns the ins and outs of it's training data and it is able to make more informed guesses. Chess is fun and all, but code generation has the potential to be a lot better than just writing functions. By feeding the LLM the AST representation of the code, the tree of workspace files, public items, module hierarchy alongside with the code, it could be a significant improvement.
There are still a lot of people who deny that (for example Bender's "superintelligent octopus" supposedly wouldn't learn a world model, no matter how much text it trained on), so more evidence is always good.
> There is the FEN notation in which in every move the entire board is encoded.
The entire point of this is to not encode the board state!