The title of the article is "Sorry, men ARE more brainy than women (and more stupid too!) It's a simple scientific fact, says one of Britain's top dons" - note the bolded part.
The article makes two independent claims, only one of which is relevant to the social/political topic being discussed (lack of women in top positions):
There are more males with extremely high IQ compared to female (which is counterbalanced with having a lot more men with extremely low IQ compared to women).
In scientific terms, the IQ distribution has fatter tails in males.
There are astonishingly few studies (due to political sensitivities of the topic) either confirming or denying that, but the main one cited is usually the Scottish early 20th century survey, which is exceptional in that it looked at a vast majority of children of the studied age group.

Note that there are virtually identical amount of men and women with "normal" IQ (85-120 IQ) - the differences are +/- 2% one way or the other.
But on a gifted level (typically considered to be 130-160) there are 15-20% differences at low end. The graph doesn't even show true genius levels (160+) but extrapolating the trend, it's likely that the differences are even higher (I've seen mentions of 1:8 ratios but couldn't find a reliable source on short order).
The second one is that on average, male IQ is higher than female.
Frankly, I'm somewhat skeptical of this claim myself, but don't have time to dig out studies (as the topic under discussion is imbalance of women in top positions that typically involve 130+ IQ, I see the claim as irrelevant even if true).