Sounds a lot like rescaling the display for different resolutions, especially if it happens during a game. However, I'd expect anyone here to be able to detect that and so I doubt it's the problem. Just to say what everyone else has already said, it sounds like the monitor. That sort of glitch, along with losing convergance and sharpness, is a sure sign that the monitor's on it's last legs. Providing it's not being told to do that by the graphics drivers that is, and changing resolutions (as can often happen in game, especially at load or when cutscenes are involved) can for some monitors cause some shifting of the display area.
And I'm 99% sure the little button he's hitting is the degausse button.