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There are many casual and even some hardcore players that love to solo in an online game. That doesn't mean they play it like a singleplayer game. In EVE, all I did was trade, socialize, craft and mine. In a singleplayer game, I can do some of those things...but its all stagnant. I can't really trade (there is no real economy in a singleplayer game) and I can't socialize or do anything I can in an online game. Online games are far more fun than singleplayer games...just because of all the people around you and talking, it really feels alive.
But I also don't want to rely on having to do anything in a group. And many online companies have seen this, and have made their online game very soloable and great for casual players. WoW was first to succeed at this, as far as I know (Its my first "MMO", but I tried a few before and never liked them).
Now I'm thinking a new sub-genre can come from this. Developers have already got rid of the RP in the name. But what about something even more simpler, MOG. Massive Online Game. People seem to get confused that multiplayer automatically means everyone is forced to group with each other (when really, it means you can interact in any number of ways with other people). This would make things a lot more clearer, easier to pronounce (MOG) and quicker to type.
Really, I think MOGs are the future of the online game genre...and many online games (like GW2, WoW as two examples, and even EVE to some degree) don't ever force you to group and have already gone a good portion of being MOGs...but there is a lot of online activity within each of those games. But they still call themselves MMORPGs, which doesn't really fit.