As much as I love Clive he is absolutely a character who exists to be the butt of a joke and fundamentally does not make sense or have an internally consistent canon. So yeah the games just play on his faceplate.
One of the earliest things I imagined was him hanging out in the room with the arcade cabs at a furry convention and inviting people to play old games, and they don't realize until they say yes that they're just going to spend the whole time staring into his face. his entire expression is still visible and he's just absolutely thrilled that he's actually getting to serve his purpose so he's just beaming at you the entire time (no pun intended) and it's very uncomfortable
but jokes aside if i had to pick any kind of "logical" explanation it would be that he's an incredibly advanced far-future sentient AI who's glued inseparably to an absolutely horrible computer but otherwise not really connected to it very closely. like, he has a little menu in the upper right of his field of view that he can use to turn the thing on and off and reboot it and not a whole lot more. if he wanted to play a game on himself he'd have to go stare in a mirror.



