DataStore isn't loading the stat?

There are a number of problems with your script.

• You do not use the player's character, but wait for it anyway
• You do not wait for the leaderboard script to insert the "Leaderstats" object into the player. You should use WaitForChild in that case (with a timeout in-case something goes wrong). Since you're accessing multiple children, it may be worth using the function I wrote below.
• You call GetAsync twice unnecessarily. You should assign the result to a variable so you only need to call GetAsync once.
• You do not implement debounce on the save feature. A person could rapidly click to save repeatedly, wasting your server's requests.
• You must put datastore commands in pcall as they may error

local DSService = game:GetService('DataStoreService'):GetDataStore('Stats')
function WaitForChildren(obj, timeout, ...)
    local t = {...}
    for i = 1, #t do
        obj = obj:WaitForChild(t[i], timeout)
        if not obj then return nil end
    end
    return obj
end
game.Players.PlayerAdded:connect(function(plr)
    local skillpoints = WaitForChildren(plr, 5, "Leaderstats", "Skillpoints")
    --or could do "skillPoints = plr:WaitForChild("Leaderstats"):WaitForChild("Skillpoints")", but it wouldn't have a timeout
    if not skillpoints then print(plr, "did not receive Leaderstats.Skillpoints") return end
    local uniquekey = 'id-'..plr.userId
    --Uncomment the following line and its corresponding '--end))' if you want the player to be able to save immediately upon loading your game, even if the GetAsync errors. If it errors, this might mean that the datastores are down, so if you let the player save over it without first loading, they might lose the information stored there. Because of this, you might want to change what happens in the 'i == 5' code.
    --coroutine.resume(coroutine.create(function()
        local success, value
        for i = 1, 5 do --try 5x, once every 15 seconds
            success, value = pcall(function() return DSService:GetAsync(uniquekey) end)
            if success then break end
            if i == 5 then
                print("Could not retrieve data for", plr,", error message:", value)
                value = nil
                break
            end
            wait(15)
        end     
        if value then
            skillpoints.Value = value
        end
    --end))

    local save = WaitForChildren(plr, 5, "PlayerGui", "Options", "Frame", "Save")
    if save then
        local saveDB = false
        save.MouseButton1Click:connect(function()
            if saveDB then return end
            local success, errorMsg = pcall(function()
                DSService:SetAsync(uniquekey, skillpoints.Value)
            end)
            if success then
                save.Text = 'Saved'
            else
                save.Text = "Error: " .. errorMsg
            end
            saveDB = true
            wait(2)
            saveDB = false
            save.Text = 'Save'
        end)
    end
end) -- end for playeradd function

I also recommend against allowing players to save every 2 seconds. Per player, you get a request every 6 seconds (and a few more for the server), meaning that it's only safe to save every 6 seconds on average (per player). Though, if you don't expect players to abuse this, it's probably okay.