I'm having the same exact problem. The computer runs fine unless I run a somewhat graphic intensive game, in which case it randomly shuts off. Just to be clear, like the OP said, I'm not talking about a freeze or a crash... I'm talking about an immediate shutdown, as if the power was cut from the system.
Before doing a whole lot of research on the subject, I replaced all my fans and cpu heatsink hoping that would fix the issue... no such luck. They all needed replacing anyway though. Nothing was changed that may have caused the issue to start happening, so I'm not sure what's going on.
When it shuts down, nothing feels hot in my computer except the graphics card. I'm running a fairly old card, a GeForce FX 5950 Ultra, is it possible that if the GPU overheats it would cause a system shutdown? Maybe I need to keep that cooler?