I would definitely say that the GPU died. Would those games be likely to have simple enough graphics without an FPS limit that might make the GPU generate excessive heat and die from over heating? This is not an unknown end to a long time behaving card, after a long time, they will get too hot and cook too much, and then never turn on again, or if they do turn on, they are damaged, and will either turn off under load, or show graphics corruption, depending on where the damage is at in the chip.
The fans spinning up is a common symptom of the EC BIOS looking for a temperature signal from the Video card, and, not seeing one, turns the fans on high by default to avoid letting something over heat before doing an emergency shutdown. Similar will happen if there is no reported Fan speed on all inputs, except it will flash the NUM/Caps/Scroll LEDs in relation to the position of the fan in the chassis, to indicate which fan it's sensing troubles with.