For describing what a social game is, we can’t just deliberately fall into one description. Besides, I chose the definitions which I think suits better the current state of social games.
Sande Chen’s definition in her article The Social Network Game Boom, as an online game in which one typically plays through a social networking site. In addition, social games place heavy emphasis around the multiplayer aspect and the connection/interaction of one player to other player
Another definition coming from Social Game Design: Monetization Methods and Mechanics by Tim Fields and Brandon Cotton, takes into account the main pillars of social games for describing what it is:
A game in which the user’s interactions with other players help drive the adoption of the game and help retain players and that uses an external social network of some type to facilitate these goals.
And providing a more abstract and global definition, here I come with mine:
A game that uses and works within a social network.
I think that a social game earns its name today just only for staying inside a favorable playground we call social network. Te uses the game has of the tools provided by such networks will determine the amount of social it develops. Is hard (if not impossible) to see games that does not make any partial use of any feature of the social network the work within.