What you're referring to is actually a combination of two game design ideas, plus a UI design.
- Splitting game into multiple chapters or episodes, each with many levels in them
- Being able to select levels after you've completed them, and replay to get a higher score
- (UI) presenting the level selection as a grid
These ideas are all quite old. The first is detailed in this wiki article: Episodic video game, with examples going as far back as 1979. The key characteristic is similar to the Gillette razor model (which is an even older idea), where the first installment(s) are provided at very low cost (or even free in the case of episodic shareware games pioneered by Apogee), and subsequent episodes could be created relatively cheaply.
The second, level selection, is also an old and relatively obvious idea. Level select lets players replay earlier parts of the game, and having a "star" or high score system provides the incentive. Other ways of encouraging replays include using "par" times, or adding secret collectables.
The third is a UI idea; grid interfaces suit mobile touch interfaces particularly well. As a comparison, the game Candy Crush uses the first two game design ideas but not the grid interface, which makes it rather difficult to browse through the previous levels.