There's only One way a video game could really damage Any screen.
If you had a very old CRT TV or a modern plasma TV and you played nothing but bright, colorful video games (think mario bros.), your TV would begin to dim and wash out slightly faster. The same thing would happen if you watched nothing but cartoons.
Of course the difference would be microscopic. You'd replace the screen due to something else breaking or because it's old long before you'd need to replace it from fading. Unless you're a shmuck and bought a plasma TV, at which point it'll turn to crap soon without the help of video games.
Outside of that, it's down to a case of the gamer throwing things at the screen in rage.