7.1 means 8 speakers in total, which is the same as 8-channel sound, so your existing integrated sound adapter is okay.
However, bear in mind that you don't get true surround-sound through headphones as it's physically impossible. You will only get "virtual" or simulated surround-sound. The only true sound through a pair of headphones is "stereo" sound.
To get true surround-sound you need to use a 7.1 speaker system correctly positioned all around the room.
While I don't want to get into the merit of how well it works, there are real 5.1 and 7.1 analog headphones on the market. That means 4 or 5 speakers positioned around on each ear.