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
          • Spartan Kick <-- Addon folder!
            • e.g.
            • lua
            • maps
            • materials
            • models
            • etc

• Spartan Kick/
  • info.txt
  • lua/
    • weapons/
      • spartan_leg/
        • shared.lua
  • materials/
    • models/
      • HEVSuit/
        • hevsuit_sheet.vmt
        • hevsuit_sheet_normal.vtf
    • vgui/
      • entities/
        • spartan_leg.vmt
        • spartan_leg.vtf
    • weapons/
      • spartan_kick_leg.vmt
      • spartan_kick_leg.vtf
  • models/
    • weapons/
      • v_kick.dx80.vtx
      • v_kick.dx90.vtx
      • v_kick.mdl
      • v_kick.sw.vtx
      • v_kick.vvd
  • sound/
    • player/
      • skick/
        • foot_kickbody.wav
        • foot_kickwall.wav
        • foot_swing.wav
        • kick1.wav
        • kick2.wav
        • kick3.wav
        • kick4.wav
        • kick5.wav
        • kick6.wav
        • Madness.mp3
        • sparta.mp3

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