I can't speak to curling, but in chess the womens' leagues are there to get women involved. There are no biological advantages at play. This is a 2000 year old game they were excluded from playing until 100 years ago. So someone could put forth a good argument that it's more about gender than physical sex.
There are very few women chess players at the top level of the game. The reasons for this are debatable, it could simply be that women are less interested in chess or that women are put off by a male dominated "sport", but I've also heard that men are much more likely to have a specific type of autism that makes them especially suited to doing well at chess.
I'm absolutely open minded to the idea that women can become top level chess players and that women's titles could be made redundant, but I think it's reasonable to see the evidence of this before we say that it's an equal playing field for both sexes. I'd suggest that we should see a decent proportion of women in the top one hundred players of the world, or even the top two hundred and fifty.
Given the current ranking of chess players, it's really hard to say that women have the same chess ability as the men and I absolutely don't want that to come across as sexism, it's just factual.
There's actually a big different in mens and women's IQ distribution. Men are all over the map, from extremely dumb to extremely smart, but women tend to statistically cluster in the middle with comparatively few outliers. Way less mentally deficient, very few Bobby Fischers.