I can't really give a great answer to that, pretty sure it was all just electrical hardware. I'm curious now, I'll look around and let you know if I find something.
Edit: yep, no code, just circuits. Here is the original circuit diagram from Atari
The very first pong game system did not use software, which blows my mind. OP's does not appear to be the same version but it's possible this it also does not use software.
The cream soda flavor is 🔥