I believe you are making a conclusion that neither the article nor science in general makes. The differences in preference are exhibited, but whether they have a biological root (and what outcomes we should target) do not have strong evidence.
"These sex differences were larger in countries with a higher level of women's empowerment."
"We explain this counter-intuitive finding through the indirect effect of wealth. Women's empowerment is associated with relatively high levels of national wealth and this wealth allows more students to aspire to occupations they are intrinsically interested in"
Though I think the preprint's reasoning about the influence of wealth is just bad. Especially if you try to reason that wealth and better education is causing alot of women to become nurses instead of doctors.
I've done horse riding, its unique and fun but definitely not for me.
There are confounding factors here, though — it's not like the only variable being changed between two countries is a woman's empowerment.
See also, Simpson's paradox.