Does Chess disprove feminist doctrine?

In "Womenism, Chess Fairness and Sinisterism", Bruce Walker argues that women's relative lack of success in chess versus men challenges the philosophical underpinnings of the feminist movement:

In January 2003, I wrote an article "Womenism and Chess Fairness" in which I noted that because men have a strong innate superiority over women in purely spatial analytical activities like chess, no woman would ever become the best chess player in the world....

In October 2004, I wrote a follow-up article "Womenism and Chess Fairness - Redux." In this I observed that the differences between men and women accounted for the social differences between men and women. In short, I utterly repudiated the totalitarian doctrine that the reason women have not "succeeded" is because men have "oppressed" then. Chess is immune to such oppression. It is pure logic. It can be played anonymously by mail. Persecuted groups often do better, not worse, than privileged groups in playing chess.

We report; you decide.