Why is this coding not inserting the TextLabel into the SurfaceGui?

Your using StarterGui wrong, whatever is in StarterGui will be inserted into the player's PlayerGui, so you need to do something like this:

local player = game.Players.LocalPlayer

print("hello")
function OrderStart()
    local order = player.PlayerGui.Screen2.Order.Text--Fixed line
    local player = player.PlayerGui.Screen2.PlayerName.Text--Fixed line
    local LabelP = Instance.new("TextLabel",  player.PlayerGui.SurfaceGui.Frame.PlayerFrame.PlayerList)--Fixed line
    LabelP.Text = player
    LabelP.TextScaled = true
    local LabelO = Instance.new("TextLabel",  player.PlayerGui.SurfaceGui.Frame.OrderFrame.OrderList)--Fixed Line
    LabelO.Text = order
    LabelO.TextScaled = true
    print("done")
end

script.Parent.MouseButton1Click:Connect(OrderStart)

**Just so you know, this doesn't look good, for bonus I made a better looking script.

local player = game.Players.LocalPlayer--Sets a variable for the player, note this can only be used by a LocalScript
local playerGui = player:WaitForChild("PlayerGui")--Sets a variable for the PlayerGui
local screen2 = playerGui:WaitForChild("Screen2")--Sets a variable for Screen2
local order = screen2:WaitForChild("Order")--Sets a variable for Order
local playerName = screen2:WaitForChild("PlayerName")--Sets a variable for PlayerName

local surfaceGui = playerGui:WaitForChild("SurfaceGui")--Sets a variable for SurfaceGui
local frame = surfaceGui:WaitForChild("Frame")--Sets a variable for Frame
local orderFrame = frame:WaitForChild("OrderFrame")--Sets a variable for OrderFrame
local orderList = orderFrame:WaitForChild("OrderList")--Sets a variable for OrderList

print("hello")
function OrderStart()
    local LabelP = Instance.new("TextLabel",playerName)--Fixed line
    LabelP.Text = playerName.Text
    LabelP.TextScaled = true
    local LabelO = Instance.new("TextLabel",orderList)--Fixed Line
    LabelO.Text = order.Text
    LabelO.TextScaled = true
    print("done")
end

script.Parent.MouseButton1Click:Connect(OrderStart)

For more info on StarterGui go here.