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.