Is there a way to make this script shorter?

Yes, you can use a for loop and the sub function of strings.

For loops executes code for every interval provided. For instance for i=1,50 do for everything between 1 and 50 do the following lines of code.

Sub is used for strings to get certain sections of the string. Say I wanted to get the letters in between 4 and 8 in "Hello World!", I would use string.sub("Hello World!", 4, 8) and I would get "lo Wo".

For simplicity, we'll make your string "Thank you for playing!" a variable named Msg. Since the for loop needs two numbers, we'll have to use 1 and string.len() function on the Msg variable. string.len() will get the length of the string, however #"StringHere" will return the same result.

local Msg = "Thank you for playing!"
while true do
    for i = 1, string.len(Msg) do
        script.Parent.Text = string.sub(Msg,1,i) --Since i is always increasing until it gets to its final number, we'll use that as the third argument of string.sub()
        wait(1/10) --We'll wait a tenth of a second before moving on.
    end
    wait(3) --We'll wait three seconds before doing the process over again.
end

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