Okay. Looks to me like you're missing your headset entirely from the playback devices. Do you have Realtek's own audio settings software running? It should install with the drivers when you download them from the Realtek website.
Just as an example, I've included two screenshots: the first one is of my playback devices. The second is of the audio panel installed along with the chipset drivers. My audio chipset is IDT and not Realtek, so your application would look slightly different, but you get the idea.
If you have the Realtek application, try to use it to enable the headset as a playback device. If you don't have the application, I recommend downloading the full package from Realtek.
Ps. It's been a while since I've had to mess with this stuff, so someone else may come along with a quicker and better idea, but this is what I'd start with.