The EyeTV app works pretty good, but the airplay button is missing. Prior to iOS 10, the app would stream AirPlay to an Apple TV if AirPlay was selected in the control center.
With iOS 10, AirPlay on apps without an AirPlay button as part of the app now defaults to mirroring mode only; theres no way around it.
With Geniatech now owning EyeTV, they need to put in a bit of programming effort and add an AirPlay button to this app.
theweatherguy about EyeTV, v2.1.6