Getting this error: player is not a valid member of Players Not sure why?

That's because you are trying to find an object named 'player' inside the Players service, which doesn't exist. Additionally, the returned object isn't a player, it's the part that touched. Since the part that touched it can be a limb of a player, we can use the method GetPlayerFromCharacter checking if the parent of the part (the potential character model) has a player.

(On a smaller note, connect is deprecated. Please use Connect.)

function onTouched(hit)
    local player = game.Players:GetPlayerFromCharacter(hit.Parent)
    if player then
        -- Found the player!  Do your logic here.
    end
end

script.Parent.Touched:Connect(onTouched)

Also try to fix that formatting up a little bit. Your code needs to be neat and organized, otherwise you won't understand it.

This is because the BasePart.Touched event returns the BasePart that touched the part. It could be a limb, torso, head, or a part that doesn’t belong to a player. Because of this, you must use the GetPlayerFromCharacter method of the Players service. You should also use Connect since ROBLOX may remove connect soon.

local plrs = game:GetService"Players"

local function onTouch(part) -- part is our parameter
    if part.Parent:FindFirstChild"Humanoid" then -- if we find a humanoid 
        local plr = plrs:GetPlayerFromCharacter(part.Parent) -- self explanatory 

        if plr then -- make sure it’s a player, not a part that fell from the sky or something
            local level = plr.leaderstats.Level
            level.Value = level.Value + 1
        end
    end

end

script.Parent.Touched:Connect(onTouch)