The opening scene in the YouTube video is from HBP not DH2.  I just read this in the comments (a response from the creator) at the end of the video:

That first scene is an actual scene from the movies, it's one of the deleted scenes (because they thought his hurt face would give too much away about Snape being on the Light side); the song is in the half blood prince movie soundtrack and it's called "In Noctem"