This is not exactly an English language Learners question. You are clearly ably handling some very heavy duty English in your reading, so you ain't no learner! :-) It's really more one of sociology itself. That said, there are a couple of the tiniest hints in your writing that although you seem, as I say, at home with advanced reading, still English might not be your first language. So here goes (but if I'm wrong and/or telling you something you already know, my apologies):
First, my understanding is that in terms of the concept of emergence in general, there is nothing special about the social variant. So in general, emergence typically refers to the more-or-less spontaneous arising, in systems composed of large numbers of sub-components, of properties that are in some way: A) dependent upon the properties of those sub-components and the way they are configured; but B) not themselves associated with the sub-components.
Liquid water is a simple example. It is wet. And that property of wetness depends on the properties of the individual water molecules and the way they interact. But none of the water molecules are wet.
So a simple view of social emergence might replace water molecules with people, and then wetness could be the medieval battlefield rout (where a demoralized army turns from the battle and runs away). But only armies (or groups) rout. The concept depends upon individuals, but does not apply to them. Of course the large scale properties of societies of humans are much more numerous and complex than wetness of water. But the idea is the same.
OK, so to Hirshleifer. I believe what he is saying is analogous to something like the following:
A battlefield rout can easily create the illusion of a direct individual propensity “for” cowardice when no such propensity exists. So the inferences drawn from empirical tests of hypotheses concerning the bravery or otherwise of individuals are often overstated.
In other words, he's reminding us, by way of a caution, of that key aspect of emergent properties: namely, that while emergent properties do stem from the individuals' properties, they--the emergent properties--are not themselves those individuals' properties. The problem he is warning us about is really one of us forgetting about emergence in the first place. If we do, then of course we might be subject to the illusion he mentions. In the water case that could be equivalent to thinking that wetness is the same thing as the Van der Waals force instead of realizing that it merely stems from such forces (among other things).
Stanford Encyclopedia of Philosophy's article on Emergent Proprties might be of interest. (It's a long article, but even the opening three paragraphs are helpful.)
Best Answer
I believe, in this context, the term means "the way things are arranged socially", or possibly societally. It is how a social structure, or a society, is arranged - or more precisely, some part of how it is arranged, or how some part of it is arranged.
It is arguing that any such arrangement that is vitally social/shared, must by that nature be educative (or educational). I'm not 100% on the use of vitally, this all seems a little old fashioned in word choice, but I suspect it might be read as essentially or at its core in this instance.