How to make debounce only apply to player who touched the brick?

Rather than use an external Value object, you can just use a Table to store each Players' debounces individually:

local brick = script.Parent
local sound = script.Parent.Sound
debounce = {}

brick.Touched:connect(function(playerWhoTouched)
    player = game.Players:GetPlayerFromCharacter(playerWhoTouched.Parent)
    if player and not debounce[player] then
        debounce[player] = true
        play = sound:Clone()
        play.Parent = player.PlayerGui
        play:Play()
        wait(120)
        debounce[player] = false
    end
end)

One thing you can do is when a player joins make a Boolean value in their player (Players > Player > Debounce) and when the debounce should be there for them set that to true and then wait and set debounce (in their player) to false. So it checks if the player who touched it has a debounce of false and if it is true it won't work.

new script to add:

game.Players.PlayerAdded:connect(function(plr)
    local deb = Instance.new("BoolValue");
    deb.Name = "Debounce";
    deb.Parent = game.Players:FindFirstChild(plr.Name);
end;

Your script:

local brick = script.Parent
local sound = script.Parent.Sound
local debounce = game.Players[playerWhoTouched.Parent.Name):FindFirstChild("Debounce").Value;

brick.Touched:connect(function(playerWhoTouched)
    player = game.Players:GetPlayerFromCharacter(playerWhoTouched.Parent)
    if playerWhoTouched and not debounce then
        debounce = true;
        play = sound:Clone();
        play.Parent = player.PlayerGui;
        play:Play();
        wait(120);
        debounce = false;
    end;
end);

Hope this helps!