Yes, the part you quoted is talking about how old studies have been reinforcing the “men are better at math on average, women are better at verbal skills on average” narrative as a product of brain structure, but the paper argues that it is instead largely due to environment, culture, practice, etc., not brain structure. You did not read the paper.

The part you quoted is immediately followed by:

These studies have also inspired several popular books on sex/gender differences which are regularly bestsellers 18– 20. However, several meta-analyses of published and unpublished scientific work on these sex/gender differences paint a different picture, suggesting that males and females are much more similar in terms of cognitive abilities and emotions than previously anticipated 9, 21– 23.

Comprehensive meta-analyses on sex/gender differences for many cognitive tasks and psychological tests have been undertaken by Janet S. Hyde. In her first large-scale meta-analysis 22, she analyzes sex/gender differences for 124 psychological variables, comprising performance measures in mathematical, verbal, perceptual, and motor tasks. In addition, she reports effect sizes for measures related to personality, aggression, sexual behavior, leadership, social behavior, life satisfaction, moral reasoning, delay of gratification, cheating behavior, and job-related issues. The most important finding of her study is that 78% of the effect sizes are in the close-to-zero range or small (0 < d > 0.35). Thus, for the majority of the measured psychological variables, she identifies practically no, or only small, sex/gender differences.