It may or may not be a fix for all of us having problems with the youtube app for google tv until google fixes it and stops ignoring the problem.
If you open that link with your google tv and it asks you do you want to open the link with chrome or the youtube app, just select chrome and when it asks for once or always choose once and you may need to do this multiple times until you get to the option to sign in.
I suggest doing it once multiple times so if the youtube app is fixed in the future that you can go back to using it and also so it does not change the options to always use chrome or the youtube app and instead asks you each time what you want to use.
Once your signed in to the link above the interface is clunky but it does play back all the videos this way at least for me.
If it works for you share what model google tv you have in a reply below.
The mobile site does not work for me but the one that does work is the lean back YouTube site. I just make a shortcut to my home screen and then move that to my menu. This is not one of the newer Google TVs it's the original NSX-40gt. on another note: Recently I've tried the nexus TV player. The old Google TV remote actually works with it but not the keyboard. The interface is pretty good but the voice feature does not work for me at all very disappointed and guess what the old Google YouTube App was way better why did Google TV have to kill it.