Not quite. There IS a "Married Man" in "Song & Dance," but that's a completely different song.
The one that was recycled as "Music of the Night" was written for Sarah Brightman when she and ALW first became a 'thing', and she performed in an early Sydmonton Festival tryout of "Aspects of Love" with Marti Webb. That's where your clip comes from.
She performed the song in concert a few times, and then recorded it as a single, but she and ALW were divorcing their spouses at the time, the song got tied up legalities (due to its content), and it ultimately was not released.