A username and password is not required to play Shadowgun Legends.
Shadowgun Legends accounts can be linked to third party accounts though. If you think you will want to change devices or recover your account later, make sure to link your account - Google Play, Game center or Facebook accounts in the game menu.
Then you can log in again with one of these accounts and your progress is loaded.
The guide on how to restore your account can be found here: https://support.madfingergames.com/hc/en-us/articles/360008018239-I-lost-my-Shadowgun-Legends-game-progress-How-can-I-restore-it-