I would think that you can talk about a currency, even if it is not a world-wide accepted currency, from the moment that it is used as a currency, that is, as an intermediate asset between providing value, and obtaining value.  Otherwise, most small (?) countries' currencies wouldn't qualify as currencies.   The Australian dollar, the Canadian dollar wouldn't qualify as a currency, because I don't use it, I can't buy bread with it, etc...

In order to talk about a currency, you must be able to use it *in some circles* as a currency, and be able to exchange it for another currency if you "change circles".  You can do that by using a "backbone" currency (what you call a global reserve currency), but that is not necessary.  Currencies do not necessarily have to have a total order (you don't like that, do you) or hierarchy.