same as my GPU (R9) capacitor burned and 2 days later dead..
dude, you're lucky it GPU is still normal.
as far as I know, the capacitor can be as an electrical retarder or temporary power storage but I'm not sure if those functions are the same on GPU.
R in R9 denotes a resistor NOT a capacitor.
A capacitor opposes a change in voltage, it doesnt retard it. It can also be used to block certain frequency ranges and smooth ac out of a dc power supply.
Id need to see a schematic to tell you what exactly the burned capacitor the OP showed is for but since the GPU works ok, my guess would be that its for a video or audio output signal.