Obviously because it is quite reasonable to assume that standards of living partially cause gender distribution by making daycare affordable, allowing more paid leave, etc., whereas gender polarization would not be expected to be a strong enough effect to pull an entire economy significantly in one direction or another.

Causal modeling is a very difficult thing when you cannot perform a controlled experiment. I would be interested in your take on how you would suggest that the authors attempt to confirm or disprove this hypothesis.

Right. Precisely. Gender polarization isn't a strong enough effect to pull significantly on an economy; sputr is trying to use a spurious correlation with little value in actually predicting whether a country will have a high or low standard of living as evidence that we've all had the wool pulled over our eyes.

Assuming you mean the authors of the documentary, I'll give you a new synopsis highlighting what it's really about: Strawman arguments abound as our intrepid documentarians drag us from interview to interview to assert that it seems people conform very closely to what our stereotypes tell us to expect of them. Obviously this must be the inevitable result of our biology! Our strawman assertion of what "equality" means is defeated! There's no way our stereotypes could be self-perpetuating! People definitely don't continue to believe in the same religions or speak the same languages or eat the same food or celebrate the same holidays just because their ancestors did! Propensity to speak English and believe in the Judeo-Christian God must also be biological destiny!

Per your last question, I have no meaningful suggestion for the authors of the video; they're going to have a miserable confirming or disproving anything as long as they insist on using logical fallacies to do so.