You can look at it as a generalized propensity to focus on different things, with and without encouragement present, and it starts pretty early. Take a toddler, he or she has 24 hours in a day. Some of those hours are generally going to be spent sleeping, some are generally going to be spent eating, some are generally going to be spent doing something dictated for them like riding in the car, and some are generally going to be spent paying attention to one of a number of choices available to the child. We know that people of all ages tend to enjoy doing things they feel they are good at. We also know that female children tend to pick up verbal and nonverbal interpersonal communication earlier and more adroitly than male ones. It would be my personal guess that the finite hours of self-directed or semi-self-directed play tend to wind up mattering a lot later in life. If my niece is very good at talking, and she knows it, she's likely to spend more of her time choosing to talk. Which means not only does she get better at it, she probably likes doing it more since it was her choice. If my son is very good at disassembling parts of his toys and figuring out where the pieces fit, but not as good at verbal pronunciation as was my niece, he may tend to be more likely to spend more of his time choosing to do those things, with the same ramifications.
At a certain point over the years, do you not think a propensity for having self-selected seeing how the pieces fit together in a toy may tend to lead to enjoying seeing how the pieces fit in a car, or a bridge, or a computer program? That in highly complicated fields which requires years of interest to climb in, or be successful in, that small differences in levels of interest over previous years may compound to fairly significant differences(I'm talking about being say a mechanic or a nurse in the 21st century, not a CEO, being a mechanic or a nurse are both remarkably complicated when you start to take into account all the skills you actually need to possess to be any good at them)? It seems like this would make sense in the light that the video in the OP seems to suggest that children in more egalitarian countries often settle into "gender-normative" roles at higher rates in some ways than do children that were raised in less egalitarian ones, wouldn't it? The children in more egalitarian countries were able to choose their routes on their own more frequently instead of perhaps feeling as if they were missing out on something different.