If you link to your Nintendo Account, you can continue to play using the same user data from Super Mario Run on another device.
Once you have linked your old device with a Nintendo Account, you must then start Super Mario Run on the new device and select Link when you are prompted about a Nintendo Account.
Note: If you access your play data on a different device platform, you'll need to repurchase the game to play World Tour beyond World 2-1.
Note: If you access your play data on another device on the same platform, you'll need to restore the purchase via that device's account after installing the game. No additional purchases will be required.