“Most large systems have game-like elements” because large systems, in order to stay functional, have rules, as do games. The elements that are broken, by McGonigal’s definition of “game,” is the feedback (or, to be more accurate, closely-related feedback) and the voluntariness of participation. (For example, school meets all but the last criteria for a game).
The thing about civic participation is that if you really game it out, e.g. classic “game theory,” it’s actually irrational to do things like vote in most elections. That’s why you need to reach for something above mere rationality — in my opinion, the old-fashioned notion of duty.