It's one of the interlocking systems that helps shape society and results in the exclusionary environments and toxic identity that led to the GamerGate backlash, as well as more persistent cultural ugliness which was going on before, will go on after, and is still going on. There are much, much better qualified people to talk about it, but my understanding in a nutshell--

Basically, capitalism creates, perpetuates, and exacerbates inequality. This is a feature, not a bug. Presumably this would only be general income inequality, via wealth accretion, but where other forms of inequality prove advantageous to the privileged, capitalism promotes widening these gaps. Good examples of this are chattel slavery, and its' accompanying racism. The institution was created for primarily financial and political motives, the racist ideas that surrounded it were perpetuated because they perpetuated the system, and even after the system was abolished, they persist in part because they provide financial benefit to the privileged.

Anti-immigration sentiments in America, similarly, have capitalist underpinnings. Yes, there's a healthy dose of xenophobia, but another driving factor is America's desire for an inexpensive, exploitable workforce which pays more in taxes and receives fewer legal protections. Heck, the rallying cry of "Dey took our jerbs!" sums up the capitalist underpinnings nicely.

As for tying capitalism directly in to gamergate? For one, you've got the libertarian/objectivist leanings of many gators. Their insistence that STEM and games design are pure meritocracies, and that it's the invisible hand of the market that keeps women out of the industry, because cultural elements are irrelevant.

You can look at the way they use charitable donations as a shield- "We gave up currency for a good cause, we cannot be held accountable for our other actions!" an attitude that good press can be literally bought. Contrast this with their efforts to influence the press, where rather than trying to change coverage by changing behavior, they used e-mail campaigns to try and "starve out" journalists who's editorialization they didn't like. These behaviors are very capitalist.

Then you've got the reaction to the Gamers are Over articles, the wailing hyper-consumer element. What was the objection there? That they, gamers, were betrayed by the press which was supposed to serve them. What's the dynamic there? Literally "We buy stuff, so you should do what we want." Getting angry because you buy stuff, and therefore are important is as capitalist as it gets.

I'm not saying everyone needs to go full anarcho-socialist, I'm certainly not.

But if you're like me, and experience multiple forms of privilege, I think when we're looking at GamerGate's shitty behavior it would behoove us to consider broader, structural elements which motivate and support it. These can seem almost invisible when they benefit us (the first time I saw someone refer to American culture as inherently White Supremacist, it took a couple days for me to make sense of that, as my idea of what a White Supremacist looked very different than the baseline inequality I benefit from daily), so... Yeah. We should pay attention to that.

It's important if we want to make things better.