Well, this is probably gonna be another long post. Buckle in people. Why is SJW concepts tied into this and why do people still care? Well, it relates to both what started the thing and what keeps it going. While that sounds damning though, do understand that reference and mention of SJW don't always mean that the people talking about it are just MRA types. This requires looking back at the controversy itself as a sort of historical take. Lets explore.
The Pre-formation - The Zoe Chronicles 1. The Spark
First, we have to remember what this movement itself formed out of. After a revelation about Zoe and her relationship with people in the media, people started to ask questions about the implications. Rational questions.
"She slept with a reporter? Did it impact her publicity? Does it relate to why she won her award? Does it relate to the articles about her harassment?"
Now, as journalists, the responsible way to handle this would have been to investigate a little, dig up the important information, make an official statement and then go on. Sadly, this did not happen. Instead, people started to get banned all over, videos covering it got falsely flagged down, TotalBiskit openly attacked and decried after a civil post on it, as well as his and other entire threads vanished in mass chunks and people were told, quite severely, to shut up about it entire. Of course, because this is the internet, the Streisand effect took full force and people were now interested and saw the efforts as an attack on them for daring to be curious.
This then resulted in the massive publicly lead inquiry into Zoe herself. All previous mentioned, who the guys were, how they related to her and gaming itself...Anything people could dig up about her because the media refused to do that job for those concerned, and in part out of spite for the attempts to stifle conversation.
The Pre-formation - The Zoe Chronicles 2. The Inferno
Because of the sudden huge interest in Zoe, things started to happen very quickly. More mass censorship on various gaming sites lead to confusion and outrage about what was going on. On Twitter, people lashed wildly on both sides and many tried to claim that investigating into Zoe was sexist. This was then picked up and ran by representatives of many gaming sites, and even our own Moviebob. The defense to any and all inquiry was a tactic of manipulation of outrage, using the loaded term of "sexist" or "misogyny" to try to shame and silence people asking or talking about it. On top of that, more investigation into Zoe resulted in discover of a sabotaged Pro-women gaming project, a browbeat into silence claim of harassment, and a revelation that the previous claim about her being harassed by a forum were demonstrably untrue. Oh and Phil Fish lost his mind on twitter again in a screaming foaming at the mouth rage. The result was a fanning of the spark of frustration and discontent into an inferno. People began to shift the conversation away from Zoe herself and onto the people protecting her and impeding their efforts to call out wrongdoing on her part. It also lead to people rapidly supporting the attempted Pro-women game jam and the creation of /v/ daughter, the Vivian James character many probably see around the site. Eventually all this was caught wind by Adam Baldwin of Firefly fame, and he jumped into the fray, increasing awareness and soon he coined the term #gamergate as a monicker for the new controversy in gaming itself. (Also worth noting for sheer brilliance, be it intentional or not, a gamergate is also an ant who can help a colony reproduce without the need of a Queen, possibly a jab based on the perceived notion that gaming journalism itself was being run by Quinn herself. Essentially having all who rally behind the tag saying that gaming didn't need a queen.)
Formation - Gamergate
After the name takes off, more people come into it and more people start investigating on their own. I believe it was around this time that many claims of harassment and being hacked appear, though they may have been going on beforehand as well. These claims themselves come off as not only ridiculous in nature due to various technical and social absurdities in how they happened, but further cement the idea in the gamers of gamergate's consciousness that such claims are the results of trying to appear the victim to avoid criticism as well as shame and blame all who are asking questions. Added to this the continued use of terms such as "misogynist", "sexist" "Attack on her for being a woman" and so on, and the narrative is quickly and firmly painted in a "gamers versus SJW" light that it still remains in.
Furthermore, the growing awareness of the movement and the end of the gaming media silence in order to report she was being harassed for being a woman and other general misrepresentations increase the size of the conflict by bring in many new people. As a result of the similarities to another often claimed professional victim in gaming, people start jumping in to argue against the trend in gaming news to push for SJW causes. People who had seen the way gaming journalism reported and commented on many stories, as well as the use of click-bait journalism in general, saw this as a point to jump on as well. Then the Pro-Women game jam TFYC was hacked, claimed to be in retaliation for siding against Zoe, and the outage and anger grows more.
Ongoing
As people learn about the cause of the who ordeal and the actual intent and purpose of gamergate, they tend to settle down. Indeed, many can quickly see that it was not so much the social causes being pushed that they disliked but rather the manufacturing and manipulation of outage in order to attack or deflect criticism that they hated in the media of late and that was exemplified by the major gaming news media's near universal reply to this. With the launch of "Gamers are dead" as a narrative, people uninterested thus far were then pulled in as well and even more were made aware of the rumblings of gamers that had been largely ignored or unreported otherwise. From that we have had many more revelations, up to the most recent ones of outright criminal fraud and racketeering.
Now, there is more and I might have messed up the order of some things (when zoe claimed to be hacked 6 times in the course of 24 hours or Phil Fish's impossible to upload hack), but that generally gives an overview and the how and why the SJW sentiment is here and still lingers. And sets the explanation to the questions of the OP.
Because of how people have seen the attempted to dismiss and cover up Zoe's actions by the press as simply acts of misogynists, many have come to start questioning connections to both other such occurrences of those tactics, as well as the motivations for them. The revealed connections to Silverstring media both to Anita and many already implicated because of the original investigations only made this worse, and when that mixed with those already tired of the click-bait "we are only bloggers when we are told to take responsibility" sort of journalists, as well as still ongoing attempts to paint this as simply doing it because she is a woman, many have thus lumped the entire counter-gamergate as shills abusing the emotional connections people have for social causes to, as you said, use it like a smokescreen. Furthermore, because the implications of gaming journalists being without integrity, it undermines the use of any sort of ideology from an honest interpretation to a front for the benefits that come from being a social justice parasite (essentially manipulating the passion of those who fight for social causes for personal gain.)
People, still flooding in, being impassioned, Having listened to the gaming journalist narrative, being narrow-viewed, not having the words to properly represent what they mean or just associating it all together, thus drag this up as SJW against gamers as well. Name calling of "misogynerd" and so on, as well as rampant stereotype use further result in more of the same in kind. Add in a hell of a lot of anger and ideological fervor to the mix and there you go, you have what is happening now.
As for supporting harassers, that is something I have yet to see anyone say they do. And it is not as if harassment is only from one side to the other. Both sides have many examples of people harassed and threatened and as I have argued before, it is impossible to blame the actions of nameless individuals like that on the entire movement. Hell, most I see is people dogpiling those that do threaten or harass out of concern for gamergate as a movement itself. I challenge anyone to go back in the "Quinn and conspiracy" thread and find when Anita had CP sent to her. You will find that the vast, overwhelming response from people supporting gamergate was to massively report the one who did it and publicly call it out for being horrible.
Why would someone subject themselves to that kind of torture?!
The people involved in this are the same sort of people who would complete a 200 hr game 100%, improve skills to become perfect, or dedicate themselves to a game for over a decade just to show they could. Honestly, these sorts of gamers are probably the most insanely determined group of people I can think of some days.