It's not like "TERF" or "anti-sex-worker" or other disparaging terms that nonetheless have specific meaning. There's simply no pattern to who gets called a SJW, other than that they pissed off gamergaters or MRAs.
The term may be more broadly applied in GamerGate/MRA circles or whatever, but who gives a shit? Those people are assholes, and they don't represent even a significant minority of anything, to say nothing of majority. Why should anyone care what they think, or what loaded and mangled terminology they use to describe their perceived enemies? None of those idiots would last long on HN, or any of the more reasonable communities on Reddit, much less anywhere in real life, unless they kept their outrageous and wrong opinions to themselves. Which is as it should be.
(I'm aware that there are people who claim to be fighting for social justice but are in reality weaponizing other people's struggles as ammo in their own private feuds. This is unfortunately a thing, but the right way to handle that is to recognize that they are not really SJWs, not to accept SJW as a bad thing.)
Still, I think the point of it is like calling someone a "morality crusader". Morality is good (if you don't mean "hating gays" by morality, mind you), but if someone called me a morality crusader, I'd get that they thought I was pompous, self-important and meddling in other people's business.
I think the issue is that it's hard to nail down what is "typical". I think you are certainly right, but there is "typical" (i.e. majority of feminists/people think this way) and there is "socially visible" (e.g. SRS/Tumblr, etc). When a person uses the SJW acronym they are definitely talking about the latter, but it's unfortunate if they conflate that with mainstream feminism: that men should be more affectionate and involved in parenting and not emotionally repressed in Western society, as opposed to the tripe that you find on the dumber parts of the web.