EVE indeed is a good one for playing in short intervals. Basically, there are two ways of improving your state in eve. One, in-game money. You get this in various ways, but it takes time in-game. You can buy better stuff...
The main way, however, is just time. You don't have to be logged in during this time, either. You just say what you want to learn (to shoot this gun or fly this ship, etc) and it tells you 'ok this will take x hours or x days to learn'. Get online again when that's supposed to be done, pick another skill. Repeat forever.
You do have to pay a monthly fee for it, however. But you definately can get things done in <1hr a day, or whatever your schedule may be. Most of the game is done solo, so no worrying about finding a group (Although you can do this if you want)... so you're out doing what you want to do quicker.