I don't understand, this study (presented from a biased source) just proves that there are two primary sexes, which has always been the case (not including hermaphrodites, who have the primary sex of one 'gender' and the sexual reproductive organs of the other/or they have both, for example).
Gender is still a social construction in the way that it's presented in modern culture. For example, I don't think there's any studies that definitively prove that boys like blue and girls like pink. That's an example of gender being a social construction. If we weren't so draconian about what people were allowed to like/do/dress in (particularly in the past), there would probably be far less people who identify as transgender, because our society would be freer to express itself without weird social barriers and boundaries that make little to no sense (for example, dresses actual work better for men, since they don't squish the ballsack like a lot of trousers do).
As for people who just don't feel comfortable in their sex's skin? I'm not them, so I don't judge them. They're not hurting anybody by changing their biological sex (most of which is done by hormone therapy and not actual surgery), so why should I care? Because nature didn't say we could change our biological sex? Well, guess what, nature said we couldn't cure cancer, but we're still going ahead with that.
I mean I don't think anybody is arguing that men and women don't have different bodies, or that men and women aren't different generally. But that study has nothing to do with social construction of gender, regardless of how that source tries to play it. You get butch women, and effeminate men. That's an example of how the idea of 'gender' isn't a strict binary.
I get annoyed at ultra-SJW I-identify-as-a-car tumblr stuff as next as the much person, but that's mainly because it makes a mockery of an interesting and complex system that deserves further examination.