>> He ran around the backyard using sticks as guns.

> Since sticks (in nature) have none of the function of guns, this is certainly a learned behaviour from social observation.

Certainly part of it, but I'd bet if you gave the girl a stick to play with, she'd probably start doing something like pretending it was a baby. The specific behaviors are learned, but the preferences may not be.

I suspect that if you manged to raise some boys and girls a a completely gender neutral environment without those social influences, they'd spontaneously invent primitive and somewhat disorganized versions of the same behaviors (sort of like with language, e.g. a critical mass of deaf children will spontaneously invent a sign language together if they're not taught one).