As I dug more into asnychronous gaming, I found this great paper by Ian Bogost titled Asynchronous Multiplay: Futures for Casual Multiplayer Experience, which he presented at a conference in 2004.
Bogost notes the following four characteristics of asynchronous games:
1. Asynchronous play supports multiple players playing in sequence, not in tandem.
2. Asynchronous play requires some kind of persistent state which all players affect, and which in turn affects all players.
3. Breaks between players are the organizing principle of asnychronous play.
4. Asynchronous play need not be the defining characteristic of the game.
It is a thoughtful history and analysis of multiplayer asynchronous games and has proved to be remarkably prescient in its predictions for casual online MMOGs. The historical perspective in particular is quite useful. Worth reading the whole thing.