You first need to determine exactly where the Coil Whine is coming from. Generally it occurs in the PSU, VRM of the Motherboard, and GPU Cards or any other hardware that uses lots of power to run.
All Coil whine is that certain electronic/electrical parts when under heavy loads produces noises when current is flowing through them. It is, as stated by another User, harmless and won't affect the hardware's performance.
If the Coil Whine started only after you installed your GPU card then you need to verify that it is coming from the GPU card.
It makes sense that you might hear Coil Whine when playing a game since that is when the GPU card is using a lot power to run unlike when it is at idle.
Not much you can do with Coil Whine except RMA the GPU card if it is very loud and annoying. Sometimes, in the past, User have mentioned that AMD Driver have caused Coil Whine in their GPU cards.