I have to admit that I don't know a lot about chess but I assume the decision to have separate categories for men and women has nothing to do with body strength and everything to do with other factors relating to "gender".
The majority of chess players are male. Chess is a strategy game where the goal is to eliminate members of your opponent's army until their king is fatally exposed and forced to surrender. It involves symbolic killing, which was long regarded as inappropriate for girls, and logical thinking, which girls and women were deemed incapable of. It's the same reasoning which resulted in little boys being given toy soldiers to play with and little girls being given toy dolls.
Of course, there is no prohibition on girls playing chess today, but the perception that chess is a boys' game remains. Men who were taught to play chess by their fathers and grandfathers are more likely to teach it to their sons than their daughters. Women are less likely to have been taught to play chess by their parents or grandparents, and more likely to have been taught to sew or bake instead.
So where do trans people fit in?
Well, somebody who was born male was not socialised as a girl from a young age. If anything, their father might have said, "Trevor, put those dolls down and come and learn to play chess."
For what it's worth, I think the concept of there being "boys' toys" and "girls' toys" is completely wrong, and if there was no stigma attached to little boys playing with dolls, and little girls were given equal opportunities to play chess, there would probably be fewer people with early onset gender dysphoria. I would very much like to see a world where toys are just toys, in which there would be no need for boys' and girls' chess categories, because girls would be just as likely as boys to have been taught to play chess at a young age.
But that is not the world we live in, which is why girls still need specific encouragement to play chess and study STEM subjects and, yes, compete in sports.
And although this is no criticism of you and individual trans people, who I think are victims of gender as much as anyone, I fear that this latest incarnation of gender identity theory is causing society to go backwards, not forwards, in this respect.
A hundred years ago, it was "Dolls are for girls and toy soldiers are for boys, everyone stay in your box." And clearly, girls were being "trained" to be mothers and boys were being "trained" to go to war.
In the 1970s, 1980s and 1990s feminists were saying, "No, there is no such thing as girls' toys and boys' toys. Let children play with whatever they like. Boys who play with dolls might be fathers one day and we want them to bond with their kids better than their male ancestors did. Girls might grow up and join the army. Hopefully none of them will be needed on the battlefield. So let children be children and let toys be toys."
And now, in 2023, it's, "If you were assigned male at birth but you like dolls, you may actually be a girl. If you are actually a girl it is vitally important that you get access to drugs to stop your healthy puberty and then as soon as you're a legal adult you can have your penis chopped off."
WTF. How on earth is this progressive?
I'm not even exaggerating, that is literally what happened to Jackie Green.