I am not going to weigh into the substance of the debate, simply because it is not my area of expertise. By that I am focusing on the single quote "Men and Women's brains are had-wired very differently ... ", which is quite a definitive claim. And to make such a claim (or to disprove it) requires a specialisation in neuro-science, or at least access to the relevant literature.
In my own personal experience, I haven't noticed a difference between the way males and females play the game. I've never looked at a move (or a game) and thought "that move was particularly male". Strong moves are strong moves, and weak ones are weak, and that is generally all I have seen. The closest manifestation I have seen to gender affecting style has curiously been in the area of over compensation, where female players are coached/rewarded for playing aggressively, as though they would not develop this talent naturally.
And to prove nothing at all, here is a game played this evening between myself and Alana Chibnall. The fact that the game ended in a draw probably shows we are chess players of comparable strength, but given the collection of mistakes that occurred at various points, I am not sure what this strength really is.
Press,Shaun - Chibnall,Alana [C43]
Murphy Memorial, 21.04.2015