The man in the video assumes that for most of the history of humankind, women have chosen who they sleep with. I'm not really sure I could support that because even going as far back as my grand mother, people in her generation had very little choice who they reproduced with.
Secondly, some traits are brought about through environmental cultivation and not encoded in genetics, a similar argument for the existence of a Gay gene would suggest that it is something that is 'passed' down through genetic inheritance but of course we know that homosexual men cannot reproduce organically.
You are correct. He specifically says women in the Western cultures have been in the driver's seat reproductively for a very long time. I think that was not the case in Eastern and other cultures up until recently, but it certainly is now. So choose carefully for the sakes of your daughters in future generations :-)