I've smashed my tablet screen today, how can I get back into the game from another device?

If you have previously bound the game then you can reload it on any other device. You will need to install the app and start a new game. Play through the initial scenes until you reach a point that you can access the menu on the lower right.

Go to the settings menu and then 'Account' and chose switch account. You can then log in again with the service you used to bind the existing game.