I can't offer much for any fangames aside from the Another series, as that's the only one I'm familiar with. I would think that each game/series, there would be a separate continuity that would need a separate fandom tag.

For this series in particular: it's designed to slot neatly into the canon timeline, even featuring some cameos of canon characters, so fans of the series treat it as a self-contained extension of canon. The games are structured almost identically to the canon games and therefore engenders basically the same fannish enthusiasm and creativity. Now, I don't know how that compares to fandoms that stem from more traditional fanworks as I've never been in one. Maybe this can be helpful anyway?