Why is my localscript running for other players?

So I have this localscript that opens a shop in the player's screen but when i run a test with 2 players both players got the shop gui when only one player touched the shop opener. Its a local script so I don't see why both players are getting the gui. Here is the script:

    Players = game:GetService("Players")
    LocalPlayer = Players.LocalPlayer
    PlayerGui = LocalPlayer.PlayerGui
    Detector = game.Workspace.ShopDetector
    RS = game:GetService("ReplicatedStorage")

ShopOpen = false
 
Detector.Touched:Connect(function()    
    if ShopOpen == false then
    RS.Shop:Clone().Parent = game.Players.LocalPlayer.PlayerGui  
    ShopOpen=true
    end
end)
 
PlayerGui.ChildRemoved:Connect(function()
    ShopOpen = false   
end)

I thought localscripts only run for the individual client... I'm really confused and questioning what localscript really is. Help is greatly appreciated.