The reason that men take most chess competition victories is mostly due to their vastly greater number partaking.
Yes, men dominate chess, because "women can't play" and so they don't play. (There are some good female chess players, but exceptions don't disprove the rule.)
"Although the performance of the 100 best German male chess players is better than that of the 100 best German women, we show that 96 per cent of the observed difference would be expected given the much greater number of men who play chess." Your link is stupid, the kind of stupidity that can only be explained by political correctness.
First, your link doesn't address the highly relevant issue of why more women don't play chess in the first place, "Our study does not deal directly with the reasons why there are so few women in competitive chess." Second, your link wrongly assumes that chess players are randomly selected from the whole population. If men and women have equal chess potential, and given that chess players are self-selected especially by aptitude, then women should be over-represented in the top 100 vs. their participation rate. Yet, they're not even equally represent. The male talent would be more diluted.
And, if it's not too much, try to remember that chess isn't the issue here. I only offered chess as one of many examples. Women spend as many hours playing video games as men do, but professional video game players are nearly all males - just as another example. Feel free to offer a counter example or an explanation other than the on I've given (whining that the participation rate is lower both begs the question and doesn't stand scrutiny).
Women lack both the physical strength and the mechanical reasoning skills that combat requires. Not to mention that they have a very high rate of getting knocked up when they're called upon for combat.