Though i disagree with your interpretations, that's a perfectly adequate description of how the name might have come about, however it does nothing to explain the choice at acronym-ize it.
I have heard people complain about the War on Drugs many times (and i often agree with those criticisms.) However i can't ever recall anyone complaining about the "WoD". Certainly not for the first reference to the name in any case. In contrast i've seen "SJW" used dozens or scores of times, but can't recall "Social Justice Warrior" being used at all except on the rare occasion to explain what SJW actually stands for. (Notably in your explanation above you just assumed everyone already knew what SJW stood for when you explained the derivation.)
So to get back to the original comment that prompted the question in this thread, why is it:
"Who are possibly outnumbered by professional victims and SJWs."
"Who are possibly outnumbered by professional victims and social justice warriors."?
or to use your own definition, why not just:
"Who are possibly outnumbered by professional victims and militant misandric idiots."?
To me, #1 sounds stupid, #2 sounds a little hokey but okay, and #3 sounds perfectly reasonable (given the viewpoint of the person supposedly saying it.) I would certainly have gone with "militant misandric idiots" myself but would be boggled by the idea if anyone suggested abbreviating it to "MMI".
(I was originally going to suggest "militant misandric assholes" as an alternative, but then realized that if you tried to abbreviate that everyone would think you were talking about martial arts. Although perhaps choosing a term that can't be acronym-ized without confusion would be a good way to help prevent that from happening.)