Chess is not segregated by gender. There are women’s tournaments and there are open tournaments. There are no men’s tournaments. Men are way overrepresented at all the open tournaments, but women do compete in all of them.

Women’s representation is increasing at the top levels but it’s a gradual process. Judit Polgar and Hou Yifan (侯逸凡) are so far the only women to reach the top 100 players in the world and regularly compete with success at the top open tournaments.

The main world championship and title of GM is open to everyone, so it's not truly split.

There are FIDE women only tournaments but that's due to there being less participation of women. When you have something like this where the skill distribution is gaussian, if you have like 50 women compete and 1000 men, you will notice that it's extremely unlikely for a woman to ever reach 1st place just due to statistics. Replace women and men with brown hair and blond hair and you'd see the same phenomenon.

The tail of the statistics where you see extreme deviations of improved skill would be dominated by the population with much larger participation.

To counter this, they have women only tournaments so that you always have a woman in 1st place in some tournament, basically to improve participation and convince more girls to play when they're young.

There are of course probably other factors but these things improve participation and are meant to help get more women in chess, not separate them out.