Trick via: ▶ How to pair a desktop or laptop to youtube.com/pair – YouTube.
This trick uses the Opera Mobile Emulator.
Note that not all settings work. The Asus Nexus 7 emulator worked, but custom didn’t always work (that would open m.youtube.com as www.youtube.com/?nomobile=1 hence switching off the mobile client).
When following the steps at Pair your mobile device to your TV – YouTube Help, you are directed to m.youtube.com/select_site to select your TV and enter a pairing code.
Usually you need to retry playing a video a few times: my Philips 42PFI7676H-12 didn’t always work at first (maybe playing back streamed video inside the emulator is not supported, but telling Youtube to pass the play request to your TV is), whereas with my Google Nexus 4 it always works.
You can even pair one computer to another: on the computer that emulates the TV, browse to www.youtube.com/leanback.
–jeroen