Yes, you can easily log in on another device with your login data and continue playing with your game scores there.
Each game has its own user profile, which can only be used to log in to that game. The player accounts cannot be linked between the different apps. With the exception of Checkers, all other games with online mode allow you to be logged in with your user account on multiple devices at the same time.
If you are logged in to a game/app on multiple devices with the same player account, you will still only be able to play in online mode on one device at a time. If you already started to play on one device and start a game on another device, the first game will be terminated. The offline mode is not affected by this and can be played at any time.
For more information on how to log in to your player account on a new device, see "How can I log in to my player account?"