It is actually exactly the same way as for the retail version of the game. The SCP only deals with the executable, the data files (discounting the media VPs) are unchanged.
Anyway, one program that will get the job done is VPview, part of the
Descent Manager toolset. Once you're done installing that and have specified the proper path for FS2, simply run VPview, select "Open .VP file" from the file menu, and pick the one that is labeled "Music data" - warble_fs2.vp. That will give you a list of all the music tracks used by FS2, with the briefing track you're looking for in particular named FS2_cinema2.wav. Finally, under the "Action" menu you have the option to extract any tracks you want.