Unless World of Warcraft on High settings, with Shadows set to Low, is stressing my GPU, I doubt that's it. In addition to that, the sound only lasts for 1-2 seconds, so it's not like it's a constant whine or anything. Another reason why I don't believe it's the result of my GPU being stressed is because I've had it occur while just sitting at my desktop while waiting for a Steam download to finish.
It occurs mostly when I game but as I mentioned in my response to the first quote, I've had it occur once while I wasn't gaming as well. Also, it doesn't sound like the sound in your video. However, I do hear that sound whenever my headset is plugged in and World of Warcraft is open. If I'm sitting at the desktop, no sound. As soon as I get into World of Warcraft, I hear that sound in my headset. Not really related to my original problem (I don't think so at least) but any idea what that could be a result of?
EDIT: Found a video that shows what sound it is. Is that a faulty PSU that should be RMA'd or is it a somewhat common occurrence that isn't really harmful?
http://www.youtube.com/watch?v=B9m3B5J41YI