To be clear, background AirPlay video only works with 1st-party Video app. It doesn't work with any 3rd-party video streaming programs (CNN, Bloomberg, etc).
I don't know whether Apple restricts 3rd-party apps from being able to stream AirPlay video in background. I had one 3rd-party app that was able to do this in 4.x, but background streaming seems to no longer work for any 3rd-party apps in 5.x