No, it does not.
The paper advances two potential reasons for the difference and selection is not one of them. Actually, genetics seem to have nothing to do with it. The two are: stress linked to the adverse environment and early disturbances in development.
"Overall, the observed association may result from exposure to an adverse environment and subsequent stress response throughout life. This would imply that sex differences in the thickness of those regions would be smaller in early development and increase during aging. This resonates with evidence highlighting the role of gender inequality in the higher prevalence of depression in girls which appears in adolescence (33)"
It's a good paper by the way. They are very careful with both their statistics and what they claim.
It does say the other part, which you wrote as adverse environment and I wrote as culture. Because the paper points out that there are environments/countries that aren't gender unequal, the entire basis of being able to do this study
To me, that basis then suggests that the unequal countries are perpetuating it far beyond culture, since people grow up and are available for mating based on some attributes over others, but you’re correct that the paper itself doesn’t go there and we dont have confirmation that the brain aspects are sex linked traits
I hope people are more willing to acknowledge the society selective forces that perpetuate every behavior we disagree with.