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I believe that it is a factor, it is far from being the only factor, probably not even the most important one. But it points in an interesting direction.
Okay, some political stuff here, because the topic is inherently political, and I even want to go one step more meta, which is deeper in politics:
Feminists have been complaining for a long time about traditional power structures in our society. Which is a legitimate complaint in my opinion, but I disagree with their choice of the word "patriarchy", because it has the unfortunate connotation that the traditional power structures are merely about something that (all? most? some?) men do to women, and so it makes us blind about things that some women do to men to maintain the traditional power structures. Suggesting that women as a group even have some kind of social power probably already is a heresy.
The list of the techniques women are traditionally allowed to use against men is here. They are mostly ad-homined arguments that a woman (for more powerful impact: a group of young women; but also their male defenders) can use against a man who tries to step out of the line.
"You are bitter!" "You hate women!" Because everyone is already primed to see men as dangerous and hateful. "You are afraid!" "Man up!" When convenient, the stereotypes of masculinity become a useful tool to shame men. "You are immature!" Grow up!" Again a reminder of failing the traditional role. "Stop whining!" "Your fragile male ego!" People have less empathy towards men, so remind them to not expect any. "You just can't get laid!" "You probably have a small penis!" Even this kind of argument is relatively accepted against men. It doesn't prove anything, it just suggests that the man is somehow defective, therefore low-status, therefore his opinions don't matter.
Each of these critiques makes more or less sense separately, but when we take them together, it becomes apparent that as a set they can be used in any situation. A man can be shamed for following his traditional gender role and for deviating from it. Maybe even both at the same time. Neither power nor weakness is acceptable. Perhaps, as a rule of thumb, a man should follow all his traditional obligations (get a job, make a lot of money, move all the heavy objects) but should not expect any traditional advantages (because that would be sexist). Even having a hobby is suspicious, unless the man can explain how the hobby will help him make more money in the future. In our culture, men have instrumental value; only women have terminal value. (Unless the man is really high-status, in which case different rules apply.)
So, in a way, if feminists complain about the traditional gender roles, they should celebrate gamers as allies, because those break the male stereotypes, and they do it on their own, no education or propaganda or change of laws necessary. But of course there is a difference between being a feminist in a sense "trying to change the traditional power structures (patriarchy)" and in a sense "cheering for the 'team women'". It's situations like this when the difference becomes visible; when weakening "patriarchy" also removes some systemic power from the "team women".
Equality comes at a price. The price is that you don't have servants anymore. If you complain about it, you probably didn't want equality in the near mode, only as a far-mode slogan.
From a proper point of view, gamers' resistance towards patriarchal shaming technuiques is an important victory of feminism. However, I would not be surprised if most self-identified feminists don't get it.
And what about women in gaming? Or gays, or asexuals? (Or course the official party line is that they don't exist.) All these people are now considered equal and respected members of the society... which includes the right to not give a fuck about what some young ladies are telling them to do.
Again, the true equality works both ways.
At least some of the attacks you describe are used against women as well-- in particular the "grow up" or "be tougher because our project is more important than your emotions" range. I'm not sure it's all as gendered as you think.
This being said, there are gendered insults (notably small penis,neckbeard, and sausage fest) that are common among feminists. I've seen some feminists argue against the first two, but not the third.
I'm wondering whether it makes sense to try to keep your opponents' identity small, and not modelling a large number of people as one big person with a unified agenda.