I know people talk about him playing 5-D chess or whatever, but the only remark I've heard from him about high level chess was demonstrably false. He said that part of why America needs to be made great again is because there are no American "grand chess masters" (sic), when in fact there's nearly a hundred American grandmasters (putting the US at #2 in the world, which is about the best we've ever been by that metric).
He has also released pictures of himself purportedly playing chess, except the board is in an impossible configuration.