Screen flickering when playing games

Hi. I'm pretty inexperienced when it comes to computers but my Sony Vaio laptop flickers when my 4 year old tries to play games (downloaded from Shockwave.com). Currently, I can't let her play the games because every time the mouse moves or something pops up (dialogue boxes etc) in the game the screen flickers and we can see numbers and letter displayed.

It's really annoying and I was wondering if anyone knew how to fix it?