As Skuzzy said, music and movies don't use the DirectSound API or DirectX. Games do.
When playing the game, your video card relies on DirectX, too. The more features you have enabled the more DirectX action goes on in your video card.
Movies go through the video card with minimal effort. As you know, a movie has everything readily made whereas a game has to draw every form, structure, skin, shadow and movement on the fly, simultaneously creating a synchronized sound environment. Even worse, movies run at 28 or 30 frames per second which is about the minimum for an enjoyable game experience, 60 FPS being the preferred speed. Further, some people already swear by frame rates of 120 or 144 Hz being superior to that.
So, simply put, it is a video card issue to some degree as you suggested, but it's not a sign of faulty hardware.
As per a DAC, it takes the clean sound "code" in a digital form outside your case, thus eliminating any static interference issues. - As you may have noticed while reading on Google, the price range of DAC's is enormous. In your case even a USB stick type external sound card might eliminate the noise, but if your soundcard has an optical output I'd opt for a little more expensive DAC with an optical input. I just read a review of DAC's where a €60 gadget equaled ten times more expensive gear by sound quality, the differences being mostly in case material and number of outputs.
The age of your amp doesn't matter. If you can get a good sound out of it from other sources, it's proven to work. Your gaming sound issues are somewhere else, most likely because of two DirextX devices struggling to give you the best gaming experience.