Why is this a 'nil value'?

There are a couple problems with this

1) - When you set the 'points' value inside of the PlayerAdded event, then it is going to get overwritten every single time a player joins. Meaning it is going to be the points for whatever player joined last.

2) - Localscript _G tables, and serverscript _G tables differentiate from one another, so you can't use it in a localscript. And I know that in that second script it's a localscript because you can only access the client's mouse from a localscript.

So what you need to do is just have the points inside the player, I know this is probably why you were doing this silly _G stuff anyways because why else would you.. but it's just going to be easier and there's no reason not to.

Script 1(make it a localscript) -

script.Parent.Text = _G.points.Value.. " Points"

local plr = game.Players.LocalPlayer
local stat = plr.Points

stat.Changed:connect(function(change)
	script.Parent.Text = tostring(change).." Points"
end)

Script 2(make it a localscript) -

local plr = game.Players.LocalPlayer
local points = plr.Points
local mouse = plr:GetMouse()
local keyName = 'GameRock'

mouse.Button1Down:connect(function()
	local t = mouse.Target
	if t and t.Name == keyName then
		t:Destroy()
		points.Value = points.Value + 100
	end
end)

Script 3(make it a serverscript) -

game.Players.PlayerAdded:connect(function(plr)
	local p = Instance.new('IntValue',plr)
	p.Name = 'Points'
end)