I feel sure that men have no intrinsic advantage in Chess, so one day there may be no need for separate women's competitions.
So far 41 women have reached the level of Grandmaster. Judit Polgar reached the world top 10, and in 2005 was one of 8 players who played in the tournament to determine the world champion.
Women have done arguably even better in Go, which also has many hundreds of professional players and presumably requires similar skills. Choi Jeong was the runner up in the Samsung Fire Cup (one of the most prestigious international tournaments) last year. The reigning British Champion is a woman and two women have won the European championship.
Surely male dominance in these types of strategic board games has been due solely to the fact that there have historically been a much greater number of male players?