Does anyone know why my laptop would turn off when I play games?
I'm not sure but I don't think it's because of overheating, I use the laptop a lot, mostly for using 3d programs and sometimes can have a lot of programs running at the same time but it works fine. Only when playing games!
I have updated my graphics driver and replaced the battery that was dying.
I'm using a Samsung R580 if that makes any difference.
I read that you don't think its because of overheating, but you should check the temperatures first because i had the same problem(on a PC) and these are generally due to overheating while playing games(high cpu/gpu usage).
So you should download speedfan- http://www.almico.com/speedfan443.exe and start it before running the game, let speedfan run in background(not inactive in tray but with its window at your desktop), play the game for 3 minutes or so(make sure you exit the game before windows turns off) and then have a look at the temperature graphs of cpu and gpu.
If its overheating there should be steep rise in the graphs towards 100/110 °. If its not anyways post the screenshots of your graphs.
If possible clear out the dust from the vents. If the bottom of the laptop feels hot after playing a game for a while, then it is overheating. I would also look into purchasing a laptop cooler which is basically a tray with two fans that you put your laptop on top of.