Reactionary means, quite literally, someone who opposes some kind of liberal reform. The reason it sways that way is simply out of historical context, with no bearing on the actual meaning of the word's components. This label is used by the crusaders because they think what they are promoting is some kind of liberal reform. It's a stupid word without much meaning, because the root of the word implies one who reacts to things. As has become evident, GamerGhazi is the group reacting to GamerGate. They are the reactionaries.

The fundamental thing to understand is that social justice crusaders understand everything in terms of collectives and politics, particularly in relative terms, and it never breaks down to a more elementary level than that unless it suits the narrative they want. So in SJ speak, whatever they believe is generally authoritatively correct, no room for doubt, questioning, discussion. Just listen and believe.

Any views that stray from this straight and narrow have to be terminated immediately, often times by identifying them as Badspeak or troubletalk, since it cannot be expected that adherents of the Correctthought are capable of evaluating the merit of ideas on their own (Were this capability assumed, SJ crusaders would permit and advocate free speech, open discussion, a fair exchange of views and ideas. But like every authoritarian group in all of history, they fight these things in order to maintain ideological purity among their numbers).

If the only way you understand the world is in terms of collectives and politics, then you have to label deviating Badspeak and Troubletalk with political and collectivist identifiers, regardless of how inaccurate they are. "Right wing", "conservative", "reactionary", etc... These terms are thrown around frequently, and they're designed to show how far off from Correctthought the trouble makers are veering. It's a particularly useful tactic when the people you're talking about are actually a diverse bunch, as far as opinions and worldviews go. There isn't nearly the ideological homogeneity among these people that is found in social justice circles, which, if acknowledged, would make it particularly difficult for social justice crusaders to group them all under an umbrella term. So these differences are ignored, and these individuals' opposition to neo-puritan authoritarianism is taken as a unifying trait that means they must all be Rush Limbaughs at heart.

You'll rarely find a fair and thorough inquiry into the beliefs or opinions or views of those who in any way oppose the SJ narrative, because that's a hassle and it doesn't serve the collectivist Correctthought efficiently enough. Fair and honest discussion will more often than not result in the SJ crusader finding an unsettling amount of rationality in their opponent, a reasoned path to their conclusions, and a level-headed cool that is difficult to slander and assault effectively. So it's best that these characteristics are left unexplored. It's easier to identify people as microorganisms of the collectives you imagine they belong to than to treat them as individuals with agency who think for themselves.

SJ in a nutshell.

Edit: I'm aware that on the surface it seems I have painted all of SJ with the same broad brush they paint their dissenters with, but there's an important distinction that has to be made. Social Justice crusaders, as I've mentioned, are all ideologically homogenous, and there is no allowed straying from the approved thought. There are very loud guiding politics and platforms that unite these people, making them more or less of the same views, opinions, feelings when it comes to everything involving social interactions, politics, etc. Their opponents, however (us), are not united by any singular ideology or worldview, and so a broad brush fails to accurately portray anything about our politics, our values, or anything else.

What they would like to believe (and this is what their whole MO hinges on) is that the reason we oppose their nastiness is because we all share some highly conservative worldview that makes us afraid of the Holy Progressive Utopia they think they are promoting. And so, in their eyes, we are a bunch of 'reactionaries' simply fighting off something that we see as a threat to our unanimously held values. This is silly and wrong, but it's what they think.