Since the whole point of this thread is the relation between gender and video games, what connection do you want me to make?
Long topics branch off from the original point, and will eventually go off topic completely.
I replied specifically to a comment about all non-physiological differences between men and woman being entirely due to society, saying that physiology has an effect beyond purely biological processes. There was no connection to make; I was stating that there are innate differences between men and woman.
If you want to know how I think that relates to gaming: it may, directly or indirectly, explain some of the difference between the number of men and women playing particular types of games. It says nothing about any particular individual (statistics or generalities never automatically do).
That statement can't be proved, and actually it's the opposite. A girl baby usually ends up with plenty of pink clothes (while still unborn), and a boy ends up with blue.
Yes, it can. Anecdotal evidence is sufficient to prove that something can happen.
If that 'usually' happens, it means the opposite 'can' happen. Some parents specifically avoid gender stereotypes with toys and colour schemes.
Same with toys, virtually no one offers a doll to a one year old boy (while my daughter already has one and she isn't one year old yet).
Boys don't get dolls, they get action figures.

So society and parents do influence toddlers.
Of course. Toddlers mimic lots of things, that's why younger siblings can be so annoying when you are a kid. I didn't claim they couldn't be influenced, I said they can like things without being told what to like.
Tomboys have grown up being constantly told to act like a lady, and effeminate boys have grown up being told to 'be a man', without that effecting the things that they like (except maybe the people doing the telling, if they are authoritarian about it).
I've managed a few times to make her use some toys instead of others, just by handling some toys more than others (or playing back).
From what I hear, there may be a period in about a year when that may not work as well.
I seem to have managed to take both sides in this nature-vs-nurture discussion because my train of thought seems to meander about rather erratically.
Well, a lot of things are going to be a mix of the two, and even if general trends indicate one or the other is dominant, there can always be individual exceptions.