After significant testing with Group Policy, we figured out that User Account Control Admin Mode has to be enabled. Yes, I know and don't ask. After enabling Admin Mode, the new Print Dialog screen appears. Later on, we started to have issues with other Windows built-in apps which showed an error, roughly stating that in order for Windows apps to work correctly, UAC must be enabled.
So, if you are having any issues with the built-in Windows apps, ensure UAC is enabled first.
Justin