BTW, something else you should never do with a laptop:
That's why there is a small movement to stop calling them "laptops" and use "notebook" instead.
I agree completely with SpywareDr's suggestion that you are having heat issues, as your shutting down during gaming (about the most demanding tasks we can ask of our computers), is a classic symptom of heat. Sadly, notebooks are very difficult for the "normal" user to keep clean of heat-trapping dust. For this reason, I don't recommend notebooks for gaming - regardless what the notebook maker's marketing department would have us believe.
If you don't feel comfortable cracking open the case (and there's no shame in that!!) take it to a shop for a professional cleaning. In the meantime, open every cover, cavity and bay, remove the battery and drives, and blast out as much dust as you can. Use a wooden glue or Popsicle stick to hold fans stationary while blasting - you can force the fans to spin faster than designed, and destroy the bearings.