How to watch unlisted video on TV:

-Log on to your YouTube account on your phone
-Tap on link in email
-Below the video, tap the like button
-Log on to your YouTube account on your TV
-Go to library and under playlist you'll see liked videos

You only have to do this once. Next time you want to watch your video just go back to liked videos under your library and the video will be always there as long as you are logged on to your YouTube account.

You can simply cast from your phone to your TV by tapping on the square with waves icon on the top right, however, you'll always need your phone to watch it and connection isn't always the best.