DirectX is used in alot of games including Source and other engines like CryEngine and Frostbite.
Download the item in the link Loke gave you, should fix it, if not, run source in DirectX 8
Gmod> Properties> Set Launch options> type ''-dxlevel 81" (it also gives you better framerate) in the thing, if that still doesn't work, you can always redownload the game and you won't even have to worry about addons because they all fucking broke.