For video playback to work, you need to be using the x86-64 chromium branch of Garry's Mod. To use this:
- Close Garry's Mod
- R-CLICK Garry's Mod in Steam and select Properties
- Navigate to the Betas tab
- Select "x86-64 - Chromium" from the dropdown
- Close the popup and wait for Garry's Mod to update