Players like Judit Polgar in chess and Rui Naiwei in Go seem to me to be strong evidence that women are not inherently worse at that sort of thing, by which I mean, if you randomly sampled 1000 men and 1000 women, and had both groups put in the same amount of effort to improve the chosen discipline (how you would practically do this while isolating for various other factors I have no idea), I would expect no statistical difference in the strength of the two groups. This does not necessarily imply that there will be as many strong female Go players or chess players as male ones, even in a utopia where everyone, so long as it is in keeping with moral behavior, is able to pursue what they desire, since a higher interest in the specific game (such as more women in Scrabble or more men in chess and Go) will affect the results, and, if the Scrabble study is accurate, different means of preferred study may also have an impact.
The claim that this is strong evidence is predicated on my conjecture that if you compare hypothetical world A in which women are inherently worse at chess and Go than men, no matter how hard they try, and hypothetical world B in which women and men are, on the average, level in chess or Go potential, but may or may not pursue those things to the same degree, the likliehood of a very strong female player in world A existing, would be much lower than the likelihood of a very strong female player in world B existing. Thus, we should assume, seeing very strong female players in these (presumably somewhat comparable) disciplines, that the world in which that observation is more likely, should be the world we most likely inhabit.
I would very much like someone who knows more statistics than me to weigh in on whether or not this is valid reasoning, and if not, if there’s a similar argument which can be made, which is not so flawed.