Im guessing that you mean the game "ESO" and that the problem occurs when running it?
If its OK otherwise this does suggest that the PSU is struggling as you are not getting a BSOD which would indicate the graphics card.
Most modern PSUs have over current protection and will shut down to protect themselves and the PC if an unusually high current is demanded that is outside their limits.
You may be right with your suggestion that the GPU current draw is causing the shutdown.
Dont know whether Corsair PSUs are good or bad but a good 750 watt PSU should cope OK with your setup.