I was asking for examples of mobile apps. There are lots of reasons that the "thin client even for singleplayer" strategy is less feasible for mobile games than for PC games.
But still, I didn't buy Diablo 3, and this was one of the reasons why.
Some examples that come to mind are Candy Crush, Marvel Puzzle Quest, Farmville, and Angry Birds. But these aren't mobile-exclusive, and they phone home to retrieve your saved game state from a database.
I'm not aware of an Android-exclusive or iOS-exclusive game that is immersive and not casual. Certainly nothing on even a Diablo-level. Anything close is multi-platform effort.
I just downloaded Angry Birds and it works fine in Airplane Mode. If Rovio goes out of business and it fails to sync my saved game to a new phone, I won't be that sad. I wouldn't say it falls under the "thin client making API calls" style software that cableshaft mentioned.
But still, I didn't buy Diablo 3, and this was one of the reasons why.