Because you don't really need a full soundcard, you just need something that has the capability of converting the raw audio stream into another digital format, and since HDMI was designed as a video+audio channel, your graphics card can do that. Plus, you have way more bandwith with hdmi: Toslink (optical) only supports a stereo stream at 192 kHz while HDMI has no problems supporting a 7.1 stream at 192 kHz.
Is your 1080 a better "soundcard" then your onboard? Not really, they are both just transmitting a digital signal without altering it. However, i can tell you from my own experience that i never experienced lags with my 1080 as the "soundcard" but had quite a bit of it when i used my onboard Realtek 1150.
And yes, you can still use your Display port, Windows just lists another playback device when you connect a hdmi device with an audio output. Since i haven't used one of those audio extractors, i don't know if it'll show (but it should, if it doesn't you can still plug the hdmi cable into your monitor (just to have a communicating device so Windows will show it as a playback device) but use Displayport as your signal source). I have my 1080 as my default audio ouput with monitors on another hdmi and a Displayport output, works like a charm.