Still the problem here is we don't _really_ know whether this is genetic or shaped by our upbringing even when it comes to the most egalitarian societies. I'd like to see the same study done on the little left hunter-gatherers bands.
No. Why do female chimpanzees prefer to play with human dolls more than male chimpanzees if it's not a DEEP GENETIC DRIVE?
On one single occasion, some female chimps were observed carrying some logs and "slapping" them. This was interpreted as playing with dolls and then it was all over the news that female chimps play with dolls.[2]
Humans aren't the only primates with culture. Chimp behaviour varies significantly according to the culture they are in, just like human behaviour does.
[1] http://news.bbc.co.uk/2/hi/science/nature/6387611.stm
[2]https://www.cell.com/current-biology/fulltext/S0960-9822(10)...