The fact that they do not credit the music leads me to believe it is an original composition. But there are a number of PC audio recorders that you could use to record that particular piece.

Barring that, you could also consider Philip Glass's score for 1931's Dracula, which is all strings, and sounds quite similar to the music you are asking about. Also similar, but with more piano, is Jill Tracy's album "Into the Land of Phantoms", which is her score for 1922's "Nosferatu". I'll try to think of more, but both of the above albums have a terrific "old timey" feel, which I think is what you are looking for.