"Handshakes" usually means "how a protocol handles direction of data". For typical serial communication, that means either hardware handshakes via RTS/CTS ( Request to Send and Clear to Send) lines, or software handshakes via XON/XOFF characters in the stream.

Since he's using "handshakes" in the context of "8 inputs / 8 outputs", I'm assuming it means he has 8 outputs that can be high or low, 8 inputs that can read high or low, plus 1 more input and one more output to handle something like CTS/RTS.

Basically, he's saying 2 lines are dedicated for hardware flow control.

And, the 8 inputs/8 outputs seem to be used like a IEE 488 (HP-IB) parallel port. He mentions talking to a Commodore PET through its parallel port. That's a little confusing because HP-IB requires 3 handshake lines, and he specifically says he has "a pair" of handshake lines. I guess it's just his own custom protocol.

He has an interface for two Pong joysticks.