I don't think apes culture-free. I suspect ape culture is highly unlikely to have gendering of wheeled toys. Mostly because that requires the discovery/invention of wheels and so on, which ape cultures outside our own have largely not managed.

It's reliable across different populations and has been demonstrated in monkeys (non-apes), for which the existence of culture may be more more doubtful.

It's pretty easy to replicate, here's an example:

https://www.youtube.com/watch?v=Bm9xXyw2f7g