Your battery is dead.
You need to replace the battery and that will fix your problem.
Why?
Because your laptop needs more power than the power brick can provide. When you play graphically intensive games you start drawing power from the battery too and because yours is dead it dies because it does not get enough power.
Get a new battery and your problem will be fixed.
Asus Rog G750JZ
Screen: 1920x1080 17.3'
CPU: Intel® Core™ i7-4700HQ (3.4Ghz @ -70mV)
GPU: GeForce GTX 880M 4GB (OC +125Mhz Core, +600Mhz Memory @ 1.062V)
RAM: Samsung 32GB 1600MHz
Storage #1: Samsung Evo 840 250GB
Storage #2: Samsung Evo 850 500GB
Storage #3: Seagate Barracuda 2TB
Storage #4: Samsung Evo 128GB MicroSD