1. That's not "a" study, it's from a metastudy. The simple fact of the matter is, while the news makes a big deal of any study that shows a statistically significant difference between genders, most of these statistically significant differences are barely above the level of noise.
2. Where are you getting that quote from the paper? A search for those words doesn't reveal that.
There absolutely are some very demonstrable differences in certain psychological regards - mainly sexual. The most obvious of these, for example, is the fact that women are more likely to be attracted to men and men to women. But that's far from the majority of studied sexual differences that get so much play in the press. " With very few exceptions, variability within each sex and overlap between the sexes is so extensive that the authors conclude it would be inaccurate to use personality types, attitudes, and psychological indicators as a vehicle for sorting men and women. "
3. Girls are far less likely to get involved in chess to begin with in all countries (again, the fact that children mimic sex distribution of behaviors of the previous generation, no matter what they are in the particular society one is in), so one shouldn't be surprised that this is reflectected in the highest levels. Chess, as a competitive sport, has always been predominantly a "men's sport", internationally. But as XKCD notes, this is changing. The Polgár sisters are a great example. Their upbringing was an experiment by their father; to see what would happen if children were raised with extensive training in a specialist intellectual topic from an early age. One ended up an International Master while the other two ended up as Grand Masters, with Judit ending up one of the world's most powerful players of any gender. Their father's choice removed gender self -selection from the picture.
4. Oh please, you're not seriously going to pretend that there weren't tremendous pressures in Victorian society for women to not be involved in STEM-style careers, or that they weren't usually expressly banned from such. Even women who took them up as hobbies (usually well-to-do women) were often strongly advised against it, that it was harmful to a woman's delicate composition to be mentally straining one's self (a risk of the catch-all Victorian women's distorder "hysteria"; the cure for "hysteria" was to refrain from all serious physical and mental activity). This is the culture that ours came from, and it's been a slow incremental process of moving away from it ever since. The fact that you'd call "citation needed" on that is absurd, that's like "A normal human hand has five digits ."
5."I'll see your 50% and raise it to 100%" - how does this even make sense? Women are 50% of the population (roughly). Nobody is talking about disinteresting men from pursuing STEM careers. There's already interest there. The goal is to try to also get more interest from women, to work against the carryover cultural connotations of STEM as "men's work".
6. " Are there laws or even customs, that prevent girls from entering a STEM field and excelling in it" - it's like you didn't even read my post.
7. "But what if it is bilogicial — as seems perfectly probable?" - not according to the actual research. And if one person wastes their time trying to become a physicist when they'd have made a better fry cook? Well whoop-di-freaking-doo. The world is still a better place.