If you have the URL of a streaming video, it's easy to display on an AppleTV, even though tvOS does not have a UIWebView (which would make it really easy). You have to use some AVFoundation code, such as:
[code lang="csharp"]
var src = NSUrl.FromString("https://somevideo");
var asset = AVAsset.FromUrl(src);
var playerItem = new AVPlayerItem(asset);
var player = new AVPlayer (playerItem);
var playerLayer = AVPlayerLayer.FromPlayer (player);
//Might want to modify this so that it's the same size as the source video
var frame = new CGRect (0, 0, this.View.Frame.Width, this.View.Frame.Height);
playerLayer.Frame = frame;
this.View.Layer.AddSublayer (playerLayer);
player.Play ();
[/code]
Note: This won't work with normal YouTube page URLs since the YouTube stream URLs are not directly accessible.