According to him, Nintendo wanted to prevent piracy so they had to add the necessity of a working internet connection. As the game will be releasing in over 150 countries, security was important for them so they added the requirement of an active internet connection to keep it safe and secure. The internet connection is a must for all three games modes of Super Mario Run.
We had thought at one point that it would be nice to have the World Tour [story] mode available standalone, to be able to play without that connection. But then the challenge is when that’s operating in a standalone mode, it actually complicates the connection back to the Toad Rally and Kingdom modes. And because those two modes are relying on the network save, we had to integrate the World Tour mode as well.
-Said Shigeru Miyamoto
So, if your mobile is on Flight mode or you don’t have access to Wi-Fi or Data Connection then you won’t be able to play Super Mario Run. One thing is that most games do require an active internet connection but that’s for once after a week or so but none of them requires an active internet connection all the time but Super Mario Run requires it and that’s a disappointing thing about it.