A friend of mine who I used to work in the computer game industry with asked me about "social games", because he has a really low opinion of them (as do I of many of them.) He wondered if they were even games at all. Here is my response to him:
I think the social games you talk about are legitimate (yet still badly made) games, because the computer has allowed a style of toy to become known as games. Simulation games which don't have winning or losing still count as games in general understanding. So I don't think that is a strike against those social games, unless it is a strike against minecraft in creative mode, which everyone would still call a game. Simulations aren't traditional games, but that is actually a good thing. They enter into new territory that makes "game" harder to define.
Simulation is a valid choice for a game design. The real problem with the social games is that they are stupid and badly made simulations.
If we wanted to make a general outline of what defines something as a game on a broader level, we would have to say something like, "operating within a set of rules that are arbitrarily different than real life in a dynamic simulated/modeled environment, for the purposes of entertainment"
This covers games kids play, like "house", etc, as well as simulation games, traditional games, and so forth. And RPGs which were much more about simulation than winning or losing anyway. D&D wasn't really a traditional game when you think about it.
I think it is unfair to label something a 'quasi-game'. Non-traditional maybe, or new, because they tend to be both. Ie, you never see them until the modern age, which is why they need us to redefine "game".
I think "game" is a broad and flexible enough category that we will always have to sub-define it to get to useful definitions anyway. "Oh this is a cooperative game, a computer game, a simulation game, an Rpg, an experimental game, a traditional competitive board game, a "folk" game (my new category I talk about), etc"
Read other interesting game design entries on this blog: Complexity Thresholds, One Test of a Game, My Favorite Tools when Designing a Board Game