It contradicts a strand of feminism for sure. But I feel like - and I admit I am not close to this debate (partly because, as he says early on, I am scared shitless of it, and it doesnt seem like a debate you can be "casually" involved in, as when youre in for a penny youre very much in for a pound) - feminism has evolved to acknowledge that point. Or many feminists have. Which is why there is this so much in-fighting going on.
I know a few feminists, a few fairly hardcore people who post nothing else on their FB timelines other than this stuff. And it seems among the people I know there is an acknowledgement that there are inherent differences between the genders. That is also implied by the whole "if there were more women in politics we would be able to clear up most of this mess overnight" line of thinking that seems to me to be pretty mainstream. The argument doesnt seem to be about there being no difference between the sexes, but that they should have equal rights and representation regardless of (or maybe even precisely because of) those differences.
Then you get into the whole debate about whether women naturally / genetically gravitate away from politics, and that is the real reason they are underrepresented. I dont believe that. Or if there is an element of truth in it, its only because they are turned off of the way politics is now, so you have to overcome that hurdle to make it more balanced. He dances around this at the beginning but his implication seems to be properly old school - women arent in politics because it doesnt suit their temperaments, they are better off sewing or looking after children, kind of thing.