> Men and women, on average, differ significantly

The linked article explicitly does not take any stance on that. What the article points out is that males are more extreme in their traits, eg. exceptionally tall or exceptionally short, which in no way means that there are average differences. Even if the deviation is different, the mean may be the same.

Not that I'm saying that those differences are or are not there, but to say that the current differences are entirely due to biological differences would seem a bit naive to me.