The player is not required to enter Burgh de Rott at all to unlock this music track. It can also be unlocked at the Barrows by walking to the small gate below it and standing in the small alcove next to it. Another alternative is by walking east of the Uzer mine near the shore as shown below on the map. The music track is most likely not supposed to be unlockable in the Kharidian Desert.
This track sounds very similar to the instrumental track Laura Palmer's Theme from the Soundtrack of the television series Twin Peaks. The tracks start with identical chords and melodies, and are extremely similar. The referenced track can be heard here.
