Nope! The first time you log in to Garfield, the game will be saved onto your device. Provided you do not delete the game, you can access your save when you load it up. Accounts are not required to enjoy Garfield: Survival of the Fattest.
However, setting up an account ensures you can access your game in the future, even if you lose access to your device. It will also protect you from losing your game if you experience a crash, and allows you to play on multiple devices. Because of this, we strongly encourage setting one up.