Rules-lightness seems to me pretty relevant, but note the other design elements mentioned earlier -- and the primacy of D&D. I suspect that a long habit of taking the last bit for granted is one reason why the phenomenon is commonly called simply "old school" rather than (say) "old-school TSR games".
Some people have always favored OD&D, and the PDF releases from WotC gave more an opportunity to check it out. It seems to have especially strong appeal for those who like to take the basic framework of the original set and create a game of one's own -- the way it apparently was meant to be used.
It remains to be seen how many will still stick with the original (or games such as S&W, S&S, or E&S). For how many is it a phase of exploration from which they will eventually return, with informed perspective and new appreciation, to some other presentation?
AD&D is rules-light relative to a lot of other RPGs. The basic elements of the original set are still "in there", and the rest is mainly a polishing of material from the OD&D supplements and The Strategic Review / The Dragon. Modularity facilitates picking and choosing, a core part of the D&D philosophy.
Most D&Ders in my experience, "back in the day", did not draw a sharp distinction among editions: "mix and match" was the order of the day. That hardly anyone played AD&D strictly "by the book" (even to the extent that's meaningful), using every option, hardly stood out from general practice throughout the FRP hobby. Put another way, the DM by the book
was the Law.
That relationship with rules is, I think, germane to the design of rules and the choice by players of a text with which to start. Speaking for myself, I would consider it a waste to treat 4E that way (a matter of degree). It accomplishes the goals of the "new school manifesto" offered earlier partly via systematic integration of the components into a carefully balanced whole. Rules mastery is central to play, and the DM's reference to established rules provides the context for the players' manipulations of mechanics.
That similar claims were made for AD&D does not mean that it actually came anywhere near 4E's success in accomplishing those goals. In my opinion, it was very far from the fact.
I would hesitate to call a game that has been around in "pretty much" the same form since 1989 new school.
Is the reference to
Champions? If so, then it seems reasonable that there might be "old-school Champions" fans to whom it is significant that (e.g.) the fourth edition hardbound had almost 7 times as many pages as the original rules book, or that it cut Endurance costs in half. That's not relevant to whether the original game -- from the perspective of old-style D&Ders -- represents a significant departure in basic design philosophy.
The newer approach is not necessarily relevant to whether they enjoy the game, either. Why should every game have exactly the same design goals? The old-school view is that old D&D accomplished
what it set out to do better than alleged "improvements" -- better, in particular, than what has since been offered under the
Dungeons & Dragons brand.