In order to authenticate the application with your Google Photos account, please follow the next steps:
Step 1: Launch the app on your Apple TV
Step 2: The application shows an unique authentication code. Take note of it.
Step 3: Using any other device (your phone/tablet/computer) navigate to https://gphoto.app and enter the above code in the text field on the main page. Click "Activate".
Step 4: Click on "Sign in with Google" which will redirect you to the Google's authentication mechanism.