Computer coil whine nightmare
More useful info is here: https://www.youtube.com/watch?v=T7HsXHqtxrI 

A few things to consider


The actual source of the sound is always something that moves. That's typically not a chip but some other component. Inductors and fans are the primary sources.
For graphics card, it's typically the inductor in the power path. The amount of noise changes with the amount of current and with the duty cycle and with the amount of high frequency noise of the switching power supply. 
Unfortunately there isn't a whole lot you can do. Unless you have detailed knowledge of the modulation scheme of the power supply, you can't really change anything on the electrical side. You may be able to dab some hot-melt on the offending coils, but you'd have to make sure that you have identified the offender correctly. The hot melt glue is also a thermal insulator so the coil will get hotter which may impact performance (resistance goes up) or you may actually fry the coil. 
You may have to get some passive insulation between you and the PC. Make sure there is no line of sight between your ears and the PC. Closed headphones work well, even better with active noise cancellation. You could build a little dog house for the PC, provided there is still plenty of ventilation. This type of thing works decently well for very high pitched noises, not so much for lower frequencies
In general this just bad design on the manufacturers part. You may want to leave a bad review to warn off other people and maybe draw some attention of the manufacturer.