No HDMI option in Playback, video works fine

I decided today to try using my flat screen as a second monitor to do video tutorials on. I plugged in the HDMI and the video part works perfectly. But there is no sound. There is no option for HDMI in the playback panel (I made sure disconnect devices show was clicked. I tried updating audio and graphics drivers. I restarted 6 times. I tried three different cords.

The sound works fine with Chromecast, Roku, and ps3 so I know it's not the tv or the cords. Any suggestions are welcome because this is driving me insane.

That is there. That is enabled. The problem is there is no HDMI option. For the sound to come through the HDMI-connected television instead of the laptop speakers.