There's a lot of questions here, I'll try to answer as many as I can to the best of my ability.
First: Is this a new concept? No. A lot of web games use "timeouts" in the form of terms, action points, or limiting the total amount of actions a player can do at once to a low number. This was true 13 years ago with the online game Utopia, and is still true in many web games today, where you get x action points per hour, and different things cost different amounts of points. This mechanic is used in board games and card games, as well, though it's usually along the lines of "you can play X cards on your turn", and is usually a way to keep the game moving.
Second: What's the purpose of this? In most online games, the purpose, as Josh pointed out in his answer, is usually to balance players, and prevent someone from having an advantage just because they have more time. If one player can dominate because they can spend 20 hours a day in the game, then no one else can have a chance at winning (or having fun). There are other reasons though. It can spread the content of the game out, so players don't reach the end in a few hours (this is especially useful in MMOs, where games tend to launch without much content). In the case of web games, it can decrease bandwidth usage (bandwidth is no longer an issue, but it was a concern in the early days of the web, and that's probably part of the reason for the convention). Josh also mentions laws in some countries to prevent extended play sessions, as well as encouraging players to return to the game later. These are both valid points.
Third (and forth): Does it bring in money or help retain users? It can. The quote "Leave them wanting more" comes to mind. Forcing users to stop playing will hopefully make them want to come back, or at least give them a reason to participate in the "community" side of games ("I've used up all my points for today, let's read the forums for a bit and talk about the game"). It can also be a source of income. "Buy 100 action points for $10" Of course, this can upset the game balance by letting the rich people with free time dominate.
Finally: Does it have other applications? Hard to say. TV shows have been doing this sort of thing for years (soap operas excel at it), and TV took the idea from radio dramas ("Tune in next time to see if our hero escapes!"). Prior to that, books were often published in serial format, including Charles Dicken's novels. The wiki article about serial literature includes other examples. How to apply this idea to something that isn't entertainment is an exercise I'll leave to you.