Is the music supposed to play during the level playthrough, or only on some occasions? I don't get any music in the game, only sound effects (playing with Wine 1.7.5 on Linux x86_64).

As far as i know there is music but very little and only on rare occasions in certain levels. But I could be wrong about that. I think the "music" is 95 % ambient sound.

So what is the soundtrack provided as an add-on for the game? That rare occasions music?

There are only a handful of instances in singleplayer where background music plays, most of the time it's just ambient sound effects. When released, Halls of Valhalla included a CD soundtrack which could be played in the background of the new multiplayer levels.

I believe the OST is a mix of both of these, with some tracks expanded or added.