In western fashion, all mens button-up clothing folds left-over-right, and womens clothing folds right-over-left. Although this might not seem important, it's a very standard rule in the clothing industry that's been followed for several centruries.
Commonly, graphic artists tend to overlook this when designing characters for video games. The Winter Coats in Star Trek Online have also been subject to this type of error. It may seem like a nit-pick, but as of now all the Winter Coats being offered in Star Trek Online are technically womens clothing.
A simple reverse of the mens coats will fix this problem.
It's certainly not a game-ending flaw by any means. I'm sorry if it's not as "crucial" as having the wrong texture on a cannon uniform, or the placement of a combadge, but it IS a mistake, and one that can be fixed very easily.
It really doesn't matter, I have a jacket that buttons up on that side, it's definitely a male jacket. It's not really an error, especialy compared to some of the other STO uniform errors, TWOK ranks, or the TNG jumpsuits.