There is a DSP chip - digital sound processor - for comuters, whethat that's on the motherboard or on a discrete soundcard, that processes the sound before it goes into the DAC. This is where you simulate a bunch of soundfield effects, like what Wacken sounds like vs Radio City Hall, or having a 5.1 channel signal from your games and movies "processed" (NOT downmixed) to simulate the same effect for stereo headphones, like Dolby Headphone or EAX.* When you have your DSP somewhere on the computer, it doesn't go through USB** (forgot why, but I think it's because USB only handles 2ch PCM signals), so you need an SPDIF output as these were designed to handle such signals (as with HT receivers, until HDMI came along). You can always disable Dolby Headphone, EAX, or whatever you have running when you're listening to music and you don't get the DSP applying anything on it.
*In a stereo recording, this is done with mic placement relative to the sound source, but of course neither can fully simulate a sound coming from behind you on stereo hardware. Look up EMMA test discs on torrents, there's a soundstage test there with one guy walking around while the mic/s stay in one position, so EMMA judges can evaluate how that voice moves around the dashboard, as in some cases it may no all be on it, but sometimes change spots on the Y-Axis on some systems (that incurs more point deductions than not having as much movement on the X and Z axis as the best system in there). In any case, Dolby headphone simulates the same thing with software to add depth for positional audio on 2ch headphones.
**There are of course USB soundcards, but what distinguishes that from a DAC is that while both have a DAC chip in them for Digital to Analogue Conversion, a USB soundcard like a PCI soundcard has the DSP chip on it. The audio data can go through USB and the DSP in a Xonar U3 for example interfaces with the software on the computer (Xonar+whatever game you're playing) so the DSP can do its job.
