No, that dongle won't work. That outputs either optical or analog sound. Also your computer's internal sound card is no good for your DAC unless you want to do some soldering on your motherboard which I highly doubt.
Let's go back to basics:
Your DAC is, I assume, a USB sound-card-based DAC. It's probably a CMedia-chip-based device. You don't send "USB 7.1" to this card/DAC, the external USB device
is the sound card. USB sound cards work by plugging them into your computer, where they show up as a new sound device capable of using 7.1 surround sound. These sound signals are converted into electrical waveforms on the sound card, which we use for laser shows. If the card is not detected as a sound card, it must have a driver problem.
First things to try:
Plug your USB sound-card-based DAC into the computer, and see if your computer recognizes it. It should say it found a new device and is installing it. Another thing to do is check if your sound-card is recognized by the system. Look at
this tutorial to see how to find it in the Device Manager. Look at
this guide I made for one of those DACs to update your drivers as well.
For that iShow thing, I don't know how it works. I hear they suck as well. The above is for homebrew USB sound card DACs.