Have a look at the DC power connector under the access panel on the bottom of the laptop. I discovered that a couple of the pins had burnt out and the white connector was discolored on mine. It appears that what's happening is that, under gaming conditions, the laptop is drawing too much power to drive the CPU and GPU together, and that has caused damage the to cable over time.
I suspect that what's happening now is that the damage is causing a protection circuit to trigger the switch from AC power to battery when you try and draw the high power needed to drive the CPU and GPU together.
I've ordered a replacement cable in the hope that will be the solution. If there is damage to the DC-DC circuitry on the mainboard as well, then that may be a bigger (and expensive) issue.