This should never happen with any proper laptop. Go ahead and try out the games. If this still happens, with the graphics card stopping to work, either the graphics card is faulty that it cannot withstand temps or the motherboard is super low quality. Either way, under normal conditions, as long as you don't overclock or keep your laptop in the oven, no matter how much you game or bench on it, you can claim your warranty. I am guesing that the heat melted your motherboard.
Be sure of the following though: Since your vents are on the left, make sure that when you are gaming, in a couple of minutes, hot air should start blowing out of the vents. Generally, all cards heat up to high levels within this amount of time and the heat should be noticeable. If it is not, then you simply have a faulty fan.
As far as the cooling fans are concerned, while these would help a bit, they wouldn't help lower the temps if they are killing your laptop. These are generally designed to keep your laptop extra cool, not normal. In this sense, they would help, but not much. This wouldn't be a good solution, though.
