[SOLVED] Computer shuts down while in-game.

[Cola]

Nah, more possible to be the graphics card overheating, as the problem only seems to appear when he is playing games or watching movies = graphic heavy material. The reason that the driver update might have helped a little, is probably that they updated stuff so that the graphics card has become more efficient = less heat.

Seeing as your PC is an all-in-one (don't buy that crap ever again), it will be very difficult to fix, unless you have had previous similar experience. The hardware inside is probably put together pretty much like a laptop, also with laptop components. Therefore you will probably only have one fan, and one or two heatpipes. You will need to remove the entire fan assembly, remove the thermal grease on the GPU (do the CPU once you're in there) and apply fresh thermal grease. Several guides to this can be found on YouTube. HPs are notorious with heat-disposing problems, therefore you might need to figure out a way to let it suck in more air, and blow out more air as well.