It's just a video of iPhone 4s to appletv using logmein but honestly if your gonna go that far might as use your iphone/iPad to play the YouTube video. Even the iPad 1 can stream video to the appletv. But if you want a 2nd display on the cheap then logmein.
Maybe you'll find those options interesting:
1. ClickToFlash - Safari plugin - in general prevents Safari from loading flash content trying to load HTML5 instead wherever possible. But has the option (right click) to send the content via Airplay. Works quite well with YouTube, etc. Can be a bit tricky on other pages but highly configurable.
2. AirFlick - free application (still 0.x version = beta but well usable) - allows to send to AppleTV audio, video, image and PDF (pages as slides) files from your computer, as well as current screenshot and URL pointing to video. There're some limits with A/V formats, but there is support for wider range of formats then typical iTunes'.
3. HUDTube Video Player - not so cheap application (AppStore) - the name tells the rest. You can drag&drop YouTube, Vimeo and local clips to the app windows and it plays them on AppleTV.
+'s: history, playlists, control quality
-'s: still no support for subtitles