When you fire up the game your graphics card draws more power when it start doing the graphics and sound.
I chased random shutdowns for weeks and had two root causes.
* One was too many USB items on the same plug (wouldn't boot with them all plugged in - fixed with wall wort)
* Charging my phone. When the phone switched to full current draw (fast charge) it would make the system reboot but only when FFXIV was on. Phone now on its' own wall wort.

Does this happen with the benchmark program or only the live game?

The only other thing I see is "NVIDIA GeForce Overlay". You could try turning that off.