Apart from the music it self, I noticed that in the video the music started playing at the title screen. In the versions I tested, music only started at the animation.
I wonder if someone has a version where the music also starts at the title ("press any key") screen?
Also in this video:
https://www.youtube.com/watch?v=jw8KCH4ZdaY the guy gets the music playing with just dosbox and soundblaster as device (see minute 14 in the video: same sound as in the other video). I read here:
https://www.lspace.org/games/discworld/faq.html#part2.4 that there are different versions of the CD version out there. Maybe it's that V3 they are using? I have no clue...