i am saying that the adapter you picked and linked to would not get any sound anywhere. kane pointed out that you can still get sound out of the mobo which is correct as well. so an active adapter with no audio port would still get video to the monitor and you can still get sound out of the normal mobo port as you always have.
the adapter i linked to would give you both a video signal to the monitor as well as an audio signal to whatever you plugged into it. either will work fine and is a choice you get to make.
please note again that the adapter you linked to will not get a signal to the monitor and should not be chosen in either case.