I'm going to mute this guy who randomly joins my discord call and does nothing productive whatsoever
Why do you want to mute him?
He just stays on the Discord, eats his food and plays his own games
It is fine to mute the person if it is your discord and they are not following the rules in it.
I have nothing against him but I never bother to unmute him
You've got the right to moderate your Discord as you please. Unless his behavior changes there is not much you can do.