Fellow old guy here myself so I'm happy to help.
You'll have to log in with your account on the other PS4 and download the game to that PS4. That's the simple part. What you'll then need to do is setup whichever PS4 he'd be playing on as your primary PS4. You'll be able to play the game on either system and he'll be able to play on the one you setup as your primary.
You can absolutely play against each other between the two systems. I do it with my son all the time. We play in an online CFM together and even choose the same division so we can get multiple in-house matchups a year.