Hello, neighbor (I'm just up the road in Inverness).
The ATI HDMI Audio is the audio from the Video card for HDMI only. Your regular PC audio is the RealTek.
I see you have a Dell Alienware. In most cases we have found on the Dell forums that you must use the Dell sound drivers. There have been cases on some older Dell systems where the System Mixer (Stereo Mix) was not available but I haven't heard about this on models for the last year or two.
Check the Device Manager again to see if it lists both the RealTek and the ATI HDMI Audio in the audio devices section. If both are showing, Uninstall the RealTek in the device manager (DO NOT check the box to uninstall the drivers) then restart the PC and whwn Windows starts it will detect and reinstall the sound. If there was a corruption in Windows for the sound this will fix that. Then check to see if you can get the Stereo Mix.
Your best place for the Alienware help is the special Alienware support forum on the Dell community forum. Lots of users there that are familiar with Alienware's. Dell's forum is down right now for some maintenance but it should be up later today. http://en.community.dell.com/