Well, the whole point of soundcards/high end integrated audio now a days, at least, is that they come with a good DAC (low signal to noise ratio, thanks to isolated components), and that they usually feature a built in amp for headphones.
As mentioned, since today’s games don’t use hardware accelerated audio like they used to, the DSP is usually limited to your standard levels + gain and encoding 5.1 or 7.1 signals for stereo headphones. During the heyday of sound cards game devs were using the processing unit on sound cards to do all sorts of cool audio effects, from occlusion to reverberation, to full 3D positional audio, which is of course, amazing! OpenAL was introduced by Microsoft I think with Vista, might be wrong about that, might have been XP, but with it came the death of hardware accelerated audio. CPU’s can and do handle a lot of the audio processing that the old sound cards were capable off, but things like full 3D audio and complex occlusion still take quite a bit of processing. There might also be a lack of easy to use API’s to get similar results in OpenAL.
A lot of people swear by external amps rather than soundcards or high end mobos with good integrated sound though. But with a good set of headphones you want something with an amp and you want a low signal to noise ratio. As for Surround Sound encoding algorythms, your mileage may vary. Here’s a decent look at what they sound like (make sure you turn off any surround effects on your headphones first!): SBX vs. CMSS-3D vs. Razer vs. Dolby vs. Realtek - headphone game sound test - YouTube
Some of these are only available with soundblaster hardware or with usb headsets that do DSP themselves. That guy’s channel has some videos discussing several of the popular soundcards.