I'm also getting this message:
The Apple TV's "Require Device Verification" setting is turned on. Because only Apple devices may provide verification, this setting must be turned off to use Airfoil with the Apple TV.

Turn "Require Device Verification" off in the Apple TV's Settings, under AirPlay Security.

I have the latest Apple TV with the Airfoil Satellite installed and running and Airfoil is running on a Mac with version 10.11.6