The video shows how an Arduino can be hooked up and pretend to be an ASCII keyboard. No EPROM change is needed. After powering the Arduino, it takes over control by resetting the Gigatron, navigating the menu and starting Loader. It fakes game controller signals to do that. Then it pushes a tiny precompiled Terminal program into the RAM. From there on, it sends simple ASCII codes which the board dutifully displays. This is step 1 towards interacting with the system for direct hacking.
The source code for the sketch is in GitHub. Hookup is with 4 male-to-female jumper wires, as explained on the Tutorials page.
Edit: The Arduino in turn can interface with a keyboard. Here an example with a PS/2 keyboard, using a standard library to handle the protocol.
The Arduino is a bit of an overkill here. A simple ATtiny85 will do the job just as well.