I've attempted that before and it didn't work. Tried it again just for the sake of trying.
I suppose, you're right, I DO get the option for it, but there is no audio detected from it.
I've tried downloading different versions, once with the Audio Redirector, then again without it after a clean install. I have tried changing my output settings to both Audio Redirector as well as Headphones. Still no dice.
This is an issue I've been experiencing off and on for years and it's rather frustrating.