A lot of great suggestions!

Back in the days there were a lot of simple platform games that you could play for 10 minutes, 

wandering off doing something else, come back and play another round. 

Roboids II comes to mind (Was there ever was a Roboids I btw?)

Glypha was another one.

Besides the obvious difficulties to implement a touch interface, many of those old games would

do great  on ios.