Here's the problem as I see it;
That particular display looks like it has over 150 individually addressable LED's in it. The LED-Wiz could drive it, with the right software, but it would take 5 of them to get the job done. It would probably react a lot smoother than the clip shows, but not worth it for what you want to do.
That chip basically does an A/D conversion and then drives the outputs based on the analog levels of the input. IOW, it needs analog in, not digital. So what you will most likely need is one chip for each column of LED's and the appropriate capacitors to filter out a specific frequency band of audio as an input for each chip.
And if that's your setup in the video, the specs state that the output of the chip is current limited, so you probably don't need those resistors for the LED's (but double check before taking my word

)
*edit*
One other possibility (that I just now considered

) Is whether or not the PWM output of the LED-Wiz would be averaged by the A/D converter and as a result, drive the display accordingly. If so, the PWM levels of the outputs could indeed drive such a display (again, with as many chips as you want "display bands" using as many outputs on the LED-Wiz)
But I don't have one to try. And if you do, I'd love to hear whether it works or not

RandyT