In the latter case, the chess example would tend to support the Bitter Lesson, rather than refute it.
I would also be VERY slow to claim that general-purpose models will never be competitive at chess. It wasn't so long ago that transformers couldn't add two-digit numbers reliably without resorting to tool use. They are now as good at "mental arithmetic" as any human savant. It wouldn't surprise me at all to see someone come up with a model that just happens to be really, really good at leveraging the portions of its general training data having to do with chess.
In fact you could argue that AGI demands such a model, if we are to assume that LLMs are a guidepost in that direction.