Yes, you can. Make sure that Cloud synchronization is turned on in game Options on the device that has your progress.

Then do the following on the second device:

1. Go to the Settings of your device and log into the same Google account.
2. Install King of Thieves from Google Play Store.
3. Start a new game and complete the tutorial.
4. Open game Options and turn on Cloud synchronization on the second device.
5. Progress restoration message should pop up. Tap "Yes".

If you are still unable to play on another device under the same account, please check all cloud save settings and make sure that it is enabled on both devices. Also, check whether it is possible to restore the progress on some other Android device besides the one you try to transfer progress to.