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

Essentially the “program” was baked into the hardware design itself. It didn’t have a rom chip or something, it just had hardware circuits dedicated to each function, like drawing the paddle etc.

It used transistor to Transistor logic or ttl, which means chips are wired together on the board to build the "code" and handle Inputs and Outputs, because affordable CPUs, ram or storage did not exist when the first arcades came out. However with more complex games this became increasingly expensive because each additional chip caused costs for parts, soldering work, warranty, potential failures during operation.

Start with googling "pong chip". There is a Wikipedia article about it, and then look for the chips "name" AY-3-8500, under which you will find lots of information about this chip.