PSU is no good / Overheating
Why blame the poor PSU? The computer can shut down if ANYTHING overheats, not just the PSU.
CPU overheating causes shutdowns
GPU overheating doesn't shutdown generally, but throttles instead
motherboard chipset/vrm overheating can also cause a shutdown.
Measure your temperatures while playing the games. I'm leaning more towards a CPU thermal problem. Make sure your cooler is clean and that it's well seated on the CPU.