Falsifiability is about grounding out in an experiment that can be performed. Epistemic legibility is a generalization of the concept, where the arguer highlights the cruxes of potential disagreement, and points to whatever evidence they feel is convincing--whether that's experiments you can replicate, official records, expert opinions, or their own introspection.
"Refutability" is a more general concept than epistemic legibility, in my opinion. One can (at least attempt) to refute abject nonsense that doesn't actually mean anything by saying "that's abject nonsense, that doesn't actually mean anything."
Other arguments might depend on facts about the world, but attempt to hide those dependencies. A Gish Gallop is one such form of argument. These can be refuted, but the interlocutor has to do a lot of work to highlight the factual errors, and the reasons that the argument depends on them.
An epistemically legible argument does that part of the work for the other party, so the only thing they must do is show which premises are wrong, or which logical dependencies are invalid.
This sort of arrogant, unapproachable response is exactly what the article is addressing. You are giving no space, no consideration at all, of someone disagreeing with you.
I got the additional impression that there are bounds to how freely the reader can interpret the narrative. Thus freed from endless mental contortion to make the argument work, the reader can assume that they are not too ignorant to understand the wit of the author but actually able to judge them as lacking. - The author has not made themself beyond reproach by presenting an irrefutable argument.
I hadn't thought in terms of hostile argument... you see this in verbal argument sometimes, where a person rambles or says vaguely contradicting things to prevent themselves from alienating their fan base.
Ambiguity lets people who endorse you to contort their interpretation into something they like.
So I think their advocating for specificity makes sense, it helps ensure that the argument is about some _thing_ and you're not engaging with some unknown meta game that lives outside the argument itself.
