All you need to do is:

1. Link your game progress to your Google or Facebook in the game settings (Settings - Account Management).

Please keep in mind that a Google Play icon that you may see after opening game settings below "Аccount management" field is showing up only the fact that you will get achievements during playing the game and it does not mean that your account is already linked to Google Play services which allows you to save game progress.

2. If you linked your game account to Google, add the linked Google account in the system settings of the second device. If you linked the game account to Facebook, you can proceed right to the next step.

3. Start the game, sign into the corresponding Google/Facebook account in the game settings (Settings - Account management) and download your game progress.