That adapter is okay, but it only gives you chat, no game sounds. That means you have your ears covered when the game audio is coming through your external speakers.
If you want to use your nice PC headset like a gaming headset with game audio and chat together, you should get something called an XJacker kit. It lets you use any PC headset for XBOX gaming by putting together just the right cables and components.
They have options to connect to your TV/audio out, or to your console directly, and for HDMI also, and they have an amped kit.
And they're really cheap and good quality. I use my PC350s with the amp kit and it works great.XJacker XBOX headset adapter kits for PC headsets