Dolby Home Theater is a suite of Dolby features, one of which happens to be Dolby Headphone.
Well, the issue with using sound cards with S/PDIF inputs to act as headphone surround processors for consoles is that they generally can't
decode Dolby Digital or DTS signals coming through the inputs. People have tried and run into all sorts of issues. They can
encode those formats for output to an A/V receiver, though; that's what Dolby Digital Live and DTS Connect do.
Neither the Xbox nor the Wii have any headphone modes. The "surround" mode probably just enables Dolby Pro Logic II encoding on the RCA outputs. You'll still hear stereo with PL2-matrixed signals, but if you want to hear the surround cues, you need a PL2 decoder-something that the Recon3D USB is incapable of.
For that matter, it's not even capable of using the analog aux-in and outputting it without being connected to a PC. I just tried it, and all I got was silence.
It will take stereo PCM signals over S/PDIF, but again, it won't decode Dolby Pro Logic II by itself.
This forum thread may suggest a means to use it as a Pro Logic II decoder when used in PC mode, though.