This download looks like an addon. You need to extract the downloaded zip and put the addon folder in your Garry's Mod addons folder. You should end up with a directory structure similar to below:

• steamapps
  • common
    • garrysmod
      • garrysmod
        • addons
          • hl2-campaign <-- Addon folder!
            • e.g.
            • lua
            • maps
            • materials
            • models
            • etc

• hl2-campaign/
  • changelog.txt
  • content/
    • materials/
      • hl2c_nav_marker.vmt
      • hl2c_nav_marker.vtf
  • entities/
    • entities/
      • trigger_delaymapload/
        • init.lua
  • gamemode/
    • cl_init.lua
    • config.lua
    • init.lua
    • shared.lua
    • tables.lua
  • info.txt
  • readme.txt

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