Hi. Have you tried this with generic content, like YouTube or Vimeo? Some providers block AirPlay of their content for reasons of their own. Also, you should be aware of the different AirPlay modes, as described below.
Video AirPlay works in two modes. Basic AirPlay just sends the video URL to Apple TV which then streams it directly. This usually works best since there's no double transmission. You're using basic AirPlay when the video player on your device goes black and says "This video is playing on Apple TV". On a computer, you do this using the AirPlay icon that appears in the controls of a screen video player object, in the browser or other app. On iPad or iPhone, use the AirPlay controls on the right hand pane of the iOS 10 Control Center, or the AirPlay icon in the video player.
The other mode is Mirroring, which generates an H.264 video stream from the device frame buffer and transmits it over WiFi to Apple TV. This video compression inherently limits resolution, and may have trouble with fast motion. When you put the iPad or iPhone video player into full screen mode, mirroring automatically switches to basic AirPlay, and it seems to be impossible to prevent that from happening. On iPad or iPhone, mirroring is on the left hand pane of the iOS 10 Control Center. On a Mac computer, you access this mode from the AirPlay icon in the main menu bar. It lets you mirror the main display, or create a new display, extending the desktop. But remember that the data sent to the Apple TV is always being converted to a live video stream. Actual display frame buffer pixels are not transmitted, as they are to a directly connected monitor.