My experience is that replying to that kind of post at face value, and just doing a detailed factual rebuttal of it like you’re doing a class presentation, is a mug’s game, because they’ll just come back at you with a bunch of firm insistence that everything you said is wrong. Bullshit asymmetry principle and all.

They did snap out of it

It seems to me that it wasn't so much that they "snapped out of it" as that they were trying to argue in good faith from the start, and got sidetracked because of your antics.

The alt-right playbook is good stuff for dealing with alt-right people or those who employ similar tactics, but if you resort to that right off the bat without justification, then you're the one who's out of line.

You should use a carrot and stick approach. If someone is sticking to the facts, you stick with the facts, if they start doing weird psychological bullshit, then you deploy countermeasures to force them back to the facts. I don't see any weird psychological bullshit in their original comment, they're just describing their views.