Same kind of hdmi setup but without windows. Anyway... !
edit : I actually just noticed why the mini didn't have a 2nd soundcard, because it's an integrated intel soundcard which needs a dedicated firmware ! Since I don't use it because I need a digitial out connector and it has none I don't really care, but I installed the firmware anyway. But no luck for you, it's a very specialized pc, no desktop environment at all and no windows, so it still selected the usb soundcard as it did before, oh well, you'll see on your side but if it doesn't work like you want I won't be able to do anything about it anyway ! (sdl2 choice, not mine).