Okay, I think you're confusing yourself here.
Your computer DOES have a DAC - any device that outputs audio from a digital source (computer, mp3 player, CD player). It's just that onboard sound, no matter how fantastic it's made out to be by the developers, is not very good. This is because both the DAC and internal amplification chips are cheap and nasty. An external DAC will bypass these internal chips and give you a better, cleaner signal to feed to your amplification stage. A line out will use the internal DAC but not the amp, so this is what you should probably be using.
About the S/PDIF - the only option I can think of is that the software is lying. If you were really plugging the amp into a digital signal it would not produce anything even vaguely like music. Perhaps the software is changing the HP out to a line out, which would explain the change in quality. No idea where the digital comes into it. If it sounds best plug it in there.
Yes, you could still benefit from an external DAC. Whether it's worth it is up to you.