While we're on the subject of things that are like MMOGs but also kind of not, it'd be a glaring oversight to leave out one of the most popular videogame series of all time. It's often been said - by me, at least - that a Pokemon MMOG could very well be the best game in the history of everything ever. So many of the series' mechanics would work perfectly in the context of an MMOG, which makes sense because the games were designed from the ground up with multiplayer in mind.
In fact, one might even go so far as to say that the Pokemon games are essentially offline, singleplayer MMOGs, a concept that sounds a lot more oxymoronic than it actually is. As previously discussed, the factors that define an MMOG are persistence - that is, does the world go on without you - and the amount of people playing it at one time. It's true that every single game in the Pokemon series is designed to be perfectly playable from beginning to end without ever having to interact with another human being. But that goes against the very spirit of the series.
The reason why every Pokemon generation since the beginning has launched with a pair of games, each missing some of the full set of new critters, wasn't just to make die-hard fans buy the same game twice for the sake of milking their wallets (though that certainly ended up being an extra bonus). Creator Satoshi Tajiri's original vision for the series' multiplayer was supposedly inspired by seeing the original Game Boy's link cable, and realizing that he wanted to make a game where friends could do more than just play against each other.
By splitting the game's roster into two halves, Tajiri made a single-player game that had to be played in a multiplayer context in order to fully complete it: Did you want to Catch 'Em All? You'll need to find people to trade you all the Pokemon that weren't in your version of the game!