I'm currently suffering the same issue.
My Elgato HD60 is set up as a Global Source, and I have (Use Device Audio) set as well. I attempted to set the audio to the Elgato, via the drop menu, but OBS crashed each time I attempted to stream. So I set back to the default.
Upon watching the previous broadcast, the audio of the game, through the Elgato capture, was nonexistent. Only audio that was heard, bled through my mic.
Is this OBS, or Elgato software configuration problem?