I might suspect (but certainly cannot prove) that the traits that make a human good at playing chess are very different to the traits that make a machine good at playing chess, and as such I don't think we can assume that the machine skilled-chess-player will be good at lots of other things in an analagous way to the human skilled-chess-player.

And Gaius point stands before this argument as well, chess is seen as such a weak predictor that playing a game of chess or requesting an official ELO rating isn't used for hiring screening for instance.

I suspect that chess as a metagame is just so far developed that being "good at chess" means your general ability is really overtrained for chess.

Second world chess champion Emanuel Lasker spent a couple years studying Go and by his own report was dejected by his progress. Maybe he would have eventually reached high levels, but I've always found this story fascinating.

True, but I'd phrase it the other way around. The traits that make you (a human) good at general problem solving are also the traits that make you a good chess player. I do suspect, though, that there are some Chess-specific traits which boost your Chess performance but don't help much with general intelligence. (Consider, for example, the fact that Bobby Fischer wasn't considered a genius outside of his chosen field.)