Well... you are right, partly, I think, in pointing out that there's still a lot of bullshit around. However, it is known that culture is, in fact, a very powerful mechanism (I think you can come up yourself with a bunch of examples). It is sometimes quite difficult to distinguish between cultural and biological factors, however, what is interesting in this study, I think, is that did an international comparison of boys vs girls' math scores and compared these to different socio-economic factors. I have to admit, I didn't take the time to read all of it, but they actually show a pretty convincing scatter plot between gender equality index and girls' math performance relative to boys'. If you don't look at anything else, look at that plot.
What about other factors that are different between genders?
I don't know about relative levels of aggression, I guess it is pretty much established that aggression level is at least partly determined by testosterone level and related hormones. An elevated level of aggression (btw, Lorenz defines aggression as social dominance behavior) would affect professional (or leadership) ambition, but I would guess that a lot of that (missing ambition) has to do with gender roles and legislation (parental leave, etc). Language ability? I think, somebody should do a study showing that the more time female caretakers spend with the child, the bigger the gender gap. Sounds like a challenge.