I think its clear that men are far more visual, and they can manipulate the pieces with less effort than female... its just like arm strength.
?
It's well established that men are better than women at spatial visualization.
That ability probably has very little, if any, chess value.
What I see in the graphs is that almost everybody (not Nakamura or Yi) shows a bit of levelling off starting around age 13 or 14, but this diminished rate of improvement is not as dramatic in the boys.
My guess is that the leveling off has more to do with hitting 2500+ than hitting 14.