If you want men to "stop hating women," going in with "the poor women are being harassed when they play video games" is not the way to do it, because it comes with overt accusations of men either being "harassers" or being complicit in harassing by not being good white knights and defending the honor of women who find out that there are people who trash talk when playing video games online (everyone, not just women). But women just assume it is only them that get "harassed" in this way.
Here's a riddle: how do these EVIL GAMER BROS know that they are talking to a woman who is playing an online game? Some games have voice chat, but for most games it is not really necessary to play the game.
The answer is that these women out themselves as a woman in some way, where it is easily avoidable and unnecessary to engage in the actions that would out women as being women playing games.
Most likely, they are seeking attention, similar to what this 4chan post states.
But rather than adapt to the environment, far too many women demand we change the environment to accommodate them. So we get content like this, as if it is a major problem that men need to address. A waste of time, of course, as the people doing the "harassment" can be safely ignored or blocked. Who cares what some idiot says on the other end of the microphone? His "threats" or "harassment" can't actually do anything. He is just like a small yippy dog: very loud and annoying, but not a threat.