Good song. No arguments there.
First *fully* CGI - that is, the people in it were digitised representations in addition to the computer-generated graphics. There were videos that had preceded it with computer animation included, but usually this was the same chromakey-overlay stuff that had been seen for (then) 20 years. It also predated
Money for Nothing.
Money for Nothing was a damned impressive video, no doubt - but the live action parts (i.e., Mark Knopfler on the neon guitar wearing the similar headband) were hand-drawn. Max Headroom was a whole other world: Max' head was actually Matt Frewer in a latex mask on a chromakey background with sampler effects (and the video you might've been thinking of was Art of Noise's
Paranoimia - "And on drums... The Pope!"). Backgrounds were generated on a Commodore Amiga.
On a side note,
Twenty Minutes Into the Future remains one of the best bits of (relatively) recent science fiction written and filmed. "Remember when we said there was no future? Well, this is it."