Ignoring the "issues" of GamerGate and instead focusing on their tactical maneuvering, what we're seeing is an abuse of the Internet's ability to allow you to hide behind a pseudonym. In some countries, you can't get anywhere near an Internet connection without presenting your ID, such that any action taken by any IP address can be immediately traced by authorities to a specific person. This, naturally, creates a chilling effect on free speech.
(For now, I'm going to ignore Tor, VPNs, and other services that attempt to recreate anonymity as well as nation-state censorship that tries to block this.)
As much as we value the absence of that sort of chilling effect in Western Democracies, we how have people abusing their anonymity to create their own chilling effects, never mind doing awful things like calling in fake police reports that result in false deployments of SWAT teams.
Ultimately, free societies work when everybody opts into societal standards of behavior. When a few people defect from those standards, and can get away with it, then society will tolerate it for a while, but after that society will adjust to solve the problem, and that means less freedom. It's all just very sad.