Offizieller Kommentar
Loopback is the superior option - the only reason I give the instructions using those other solutions is they're free, and DJs are cheap. ;)
To get the audio from Loopback, it's pretty straight-forward; see the instructions here, the only difference being that you select the channels to route from the Source (on the left of Loopback) as the ones you've chosen as the REC OUT from the DJM's Setting Utility.