The first game, he said, was called Exam Pac-Man: since there are usually three or more invigilators in any given exam there are enough of them to have their own game of Pac-Man. Between them, presumably before the exam starts, they decide who's going to be Pac-Man and who're going to make up that team of dastardly ghosts. Since they don't have any white pellets for Pac-Man to eat, the desks used by students replace them: the person playing as Pac-Man has to walk past every desk without being caught by a ghost. That sounds like innocent fun doesn't it? Well, just wait until you hear the second one.
The second game, I can't actually remember the title of, but we'll call it The Ugly Baby Game. Basically, the invigilators look out at all of the students and the have to pick the combination of them which would produce the ugliest baby. So, next time you're in an exam, worried about what you're writing, if you've remembered enough or any other exam related anxieties, be sure to make sure you look nice, because you're physical appearance is being judged the whole time!
These're the only games he mentioned, but I find it quite amusing that they exist. I'd never assumed before that exam invigilators play any games, but, thinking now, it seems pretty obvious that they'd need something to pass the time with.