First, of course, he was such an unlikely choice to write the music and lyrics to a Broadway show. Though a very successful songwriter and performer, most notably the great song, "King of the Road," it was not only for country music, but often off-beat country music, hardly the stuff of Broadway, particularly at the time. Also, it was extremely rare for a popular singer/songwriter to write a Broadway show. It's much more common now (Cyndi Lauper won just last year, for Kinky Boots), but as far as I know, it might even have been the first time it had been done -- at the very least the first done such a person had won the Tony. But most especially, he'd hit hard times, largely due to having had a drug problem, which took him out of the mainstream for quite a while. And he'd been at the top of that stream, even having a popular national TV variety show. So, it was all the more a stretch when producer Rocco Landesman contacted him about writing the show's score -- and turned into a great triumph and return for him.
In the video, by the way, that's Landesman who you'll see Miller give a bear hug to on the way to the stage. Presenting the award is George Hearn, who the year before had won the Tony for Best Actor in a Musical with La Cage aux Folles.
(I've edited the video of the full ceremonies down to this presentation, and it should work fine, though I've had glitches testing it. For some bizarre reason, it sometimes jumps to a collage of end-images while playing over some singing from somewhere in the show. But -- if it does that, there appears an easy, inexplicable fix. Just go to the lower-left corner where you'll see a circular refresh-arrow. Click on that, and All Will Be Well. I hope. Well, enough of that, let's find out. Curtain up...)