It started as soon as 3e was out, I'd say. But it took a little while until people had grokked the idea of open licenses and com up with their own versions of the games they loved when they were kids.
There are many different appeals, it looks like to me.
One is to recreate and spread the game they used to like (the one they started with, it seems). Nostalgia.
Another to have a simpler and more open ended game, which perhaps leaves more place for imagination (or at least forces people to use their imagination, as there is notheing else).
A third is to recreate their favourite rules, but in a better, revised, dressing. Like Castles and Crusades. And Pathfinder, perhaps (or partially).
Yet another aim is to make something like the SRD, but for the preferred pre-3e edition. One of the things with the OGL is that it cannot be recalled, whatever happens people can continue to play D&D3/SRD, and make new stuff for it - so people want to make sure that is possible with their favourite earlier edition. OSRIC started out this way.
But the main appeal to me seems to be nostalgia and a harkening back to earlier, simpler, times - when dungeons were endless and monsters random.
Generally to the times when the players (and authors) were first introduced to RPGs.