Maybe, relative to boys, they do. Girls and boys are more different at age 15 than 5, and the greater differential in running speed at age 15 is not due primarily to socialization. I think it is plausible that puberty increases intellectual differences between the sexes.
Again, you're applying a false analogy and conflating physical differences with cognitive ones. Males are, on average, taller, carry more muscle mass, and have higher VO2max, among other population physical traits, that enable greater running speed than females. What gender-linked morphology is it that you purport makes males superior to females in chess on a population, not individual, basis? I'd like to see some studies to back up your premises which, though repeated in each of your replies, remain unsubstantiated.
Females are also underrepresented in men's public washrooms. Hint: the causality isn't linked to neurological gender differences.
Couldn't avoiding an activity that you would otherwise enjoy because there are too many boys (or girls) doing it be considered sexist? Our local chess club is majority Chinese, with some Indians and fewer whites (most of whom have Russian parents). If someone avoids the chess club because they don't like the ethnic mix, that's their problem, not the club's.
The club's goal is to maximize the performance of its constituent members, with minimal input (instruction). If the club has a demographic or ethnographic mix that systematically statistically underrepresents a major group at certain levels (in this case, females), it is in the club's best interest to actively encourage the participation of underrepresented groups. Otherwise, it's truncating the distribution of players it draws from, which limits the expected probability that the average inductee is a high-ability player. The result is, on average, a lower ability team that has less exposure to competing with high ability players, which is to the detriment of everyone involved.
Actively encouraging underrepresented groups' participation is
exactly what the highest performing F100 companies do to recruit a workforce of diverse backgrounds and with the best capabilities. If it works for Goldman and Pfizer, why not Main Street School Chess Club? Or, is the motive of the club twofold: maximum performance within a given demographic? Because, to me, it sounds like the latter the way you portray it, Bostonian.
By HR law in most of the industrialized west, if an underrepresented group at a firm is not explicitly encouraged to apply for a given position, discrimination is deemed present because the demographically biased environment creates a hostile climate for the underrepresented applicant. So no, it isn't sexist for a little girl to shy away from a predominantly male chess club, or a little boy to avoid a dance troupe, if the prevailing climate is exclusionary to their demographic group. If countries rightly protect adults from that sort of xenophobic discrimination, why should children be subjected to the same injurious injustice just because their social opportunity set has a less formal legal and organizational structure?!
