Beaky, that's not strictly a vibrato, but more of a tremolo, done only on the Irish Bagpipe (or Uilleann Pipes), not the Scottish ones, in general, and is done by fluttering your fingers over open lower holes on the chanter.

But it is definitely a sound that is not employed to every note in a phrase, but picked and chosen carefully, like a good use of the Leslie... (and if some notes require most of your fingers, you have none to spare for the flutter). Absolutely NEVER on just about every note, like the Yamaha demo.

Check out some early music by the Chieftains, for some pretty authentic playing (amongst many others )