not making any claims about its conclusiveness, the poster to which I was replying made an argument to incredulity to which there is actually contradicting evidence.
Since chimpanzees are relatively sexually dimorphic perhaps they are not a good way to argue against human sex differences. Also since chimps and monkeys have less sophisticated use of objects it shouldn't be surprising that the evidence has some degree of muddling but we know that there are sex differences in play behavior, such as male juveniles monkeys preferring rough-and-tumble play, or females showing more interest in the infants in their group (which the studies I cited earlier reference).
If I were to make a more general case, however, this wouldn't be the only evidence that I would rely on.
You might look at studies of very young children, younger than it is believed they would be aware of their gender:
http://jbd.sagepub.com/content/25/1/7.abstract
If you're disinclined to belief update from that, you could still say they were still influenced by culture somehow.
Going further you could look at even eye-tracking studies of infants:
http://www.ncbi.nlm.nih.gov/pubmed/19016318
If you were still disinclined, you could say there's still social influence in there, maybe, it can't be ruled out...
But then look at evidence of prenatal hormone exposure, such as digit ratio (marker of androgen):
http://www.sciencedirect.com/science/article/pii/S0191886909...
Or those with hormonal disorders:
http://www.ncbi.nlm.nih.gov/pubmed/12414881
http://pss.sagepub.com/content/3/3/203.short
http://people.uncw.edu/hungerforda/Infancy/PDF/Prenatal%20ho...
If toy preferences are socially constructed, why would an obscure endocrine disorder predict toy preference according to the hormones that boys or girls were more typically exposed to? The latter study suggests that those with atypical hormone exposure face increased socialization pressure to conform, yet which apparently shows the least influence on their preference.