There’s a slew of mobile games that users can play on their devices… and many of them can be “enhanced” by playing online against others.
However there are many times when you might not have Internet access (on a subway, in a tunnel, on a plane, at a convention where the WiFi is jammed) or any interest in wasting your data plan to update your game stats on some server somewhere.
I’m not going to name names… but there’s a bunch of games these days that *require* an Internet connection to even run!
Intelligently designed games can store your game stats locally and then upload them at a later date if desired… there’s no reason a game should force the user to be online in order to play (unless it is a critical part of the game… e.g. online chess).