I was noodling about this this morning and I wonder if a slightly different definition might not work. For me, a "working" system means that the system is reliable. In other words, I, as player or GM, can be fairly confident that in any given, fairly normal situation in the game, the rules of the game will cover the resolution.
This was always my problem with early forms of D&D. Yes, I played the heck out of those systems back in the day. Far, far too many hours. But, over the years, I managed to accrete a lot of house rules and patches for those rules. And, I'm hardly alone there. Lots of people talk about the binder full of house rules they had/have for AD&D. Fast forward to WotC D&D and now, my house rules would probably fit on a couple of pages, and most of those are table rules, not actual rules changes for the game.
If the people playing the game can be confident that introducing a new element to the game will just work, then the system can be said to work. If, OTOH, I have to vet every single element, going over it and testing it and then revisiting that new element every single time, then, no, that system doesn't work.
Although, to be fair, "the system works" should always amend the phrase, "for me" to the end. What works for one table is very much not true for other tables.