Your Garry's Mod is outdated!

You are using a version of Garry's Mod, which does not support Youtube video playback. Please change to the chromium branch to fix video playback.

Here's how to do that:

Exit Garry's Mod. Right click Garry's Mod in Steam library and click Properties

Open the "BETAS" tab, and select "chromium".

Once completed, you can rejoin the server and watch youtube normally.