Hi MyNameisNotBilly,
Thank you for using the Apple Support Communities.
We understand that you want to add the GamePigeon iMessage app to the Always Allowed list however, at this time some of the iMessages apps cannot be added to the Screen Time Always Allowed list. If you’d like to see iMessages apps added to the Screen Time Always Allowed list in the future, then we recommend that you send feedback about this here: Product Feedback - Apple. If you want up keep up with Apple announcements check out the Newsroom - Apple page.
Use iMessage apps in Messages on iPhone
Use Screen Time on your iPhone, iPad, or iPod touch
Use parental controls on your child's iPhone, iPad, and iPod touch
Have a nice day.