Hehe, I have trouble with this all the time as well. I do beat a ton of my games though. Since I can't seem to stop buying games, I use the fact that I beat one as justification to buy a new one as a way to very weakly control how much I spend on games, lol.
What happens to me is if I don't beat it, it usually stays in the back of my head that I have to beat it, lessening the fun I'm having with a new game. Plus, I just like knowing that I beat/completed something and experienced everything I could in it. I'm the same way with books, and I think that's actually where I got this "need" to finish games from. Unless the book is so horrible that I don't go further than 25 pages, I always finish a book.
Doesn't mean I beat everything though. I just try to take games to as far a completion as possible based on whether I can stand playing it anymore. For instance, Dragon Age. Loved it for about the first 25 hrs. Then it was like the graphics took an even further dump, and I slogged through the next 20 hrs. Once I got to the dwarf city, I liked it again, but once I got out, I didn't feel like playing anymore. I got to about 80% completion and I kept it installed, kept telling myself I was going to play it. A year later, I finally uninstalled it knowing that I was never going to finish it, and didn't buy the 2nd one since I knew I wouldn't play it.
To answer your direct question, I think what keeps me going in the game is to figure out everything there is about it. So yeah, like you, when I've seen everything the game has to offer, I sort of shut down. Best example is the first Assassin's Creed. I though it was the best thing ever, then the quests were the same in just a different part of the same three towns. I shut it off and never played again. Games like Torchlight though, yeah, within the first couple hours you've basically seen everything . . .except the awesome new loot you can get. That's what keeps me playing ActionRPG games all the way to completion.
Unfortunately there are very few games that keep me interested based on story alone. I don't think the game industry is all the way there yet with storytelling. Either they're massive too long and convoluted where the kitchen sink of cliches is tossed at you (jRPG's), or they're quick 5-10hr FPS romps about survival or killing the bad guy--plus everything in between like the massive story choose your own adventure games.
I think you've got to look at why you like gaming to begin with. If you like them the way you like seeing art in a museum, then yeah, you'll look, stare into it and read the little text, but not invest anymore time into it.
For me, I traveled a lot growing up. My wife got sick, money ran dry paying for medical bills, and so I haven't really been able to travel anymore outside of CA. So when I game, it's to recreate that sense of adventure of traveling to someplace new. When I travel, I like to adventure and get lost in a town and find little food dives, or little hidden places you wouldn't find on a travel book (like this mayan run underground cave system in the Yucatan where some little 8yr old kid gave us a snorkling tour, lol). So because of that, I like trying to see everything on a game map, all the locations, clear out all the black if a game has the fog of war. It's sort of OCD, yes I know.
There's nothing wrong with your way of playing though. If all you want is to stay for drinks in a game, whereas I like appetizers, main course, dessert and coffee, doesn't really matter. Like some of the other posters have said, all that matters is that you enjoyed yourself.