Google have added the ability to send videos from the iOS version of the app to a YouTube app on a Smart TV, Xbox 360 or PS3. Just as you can from the Android version you can send playing videos from the app to a paired app on the TV, Xbox or PS3. To get it working you go to the updated app and in settings you select Pair YouTube TV, on your TV you go to the YouTube app and select Pair Your Device where the TV will give you a code to enter into the iOS device.
Then you should get a little dropdown when playing a video and you can pick your iOS device or the TV. I gave it a try with my Samsung Smart TV and it seemed to play very well. The updated app can be found in the iTunes app store.
What’s New in Version 1.2.1
* Send to TV: control YouTube on TV, Xbox or Sony PS3 from the app
* Improved streaming over slow WiFi connection
* Ability to record and upload video via YouTube Capture
* Overall stability improvements