Hopefully, you replaced the throw out bearing when you did the clutch.
(did you grease the pivot ball when you reinstalled the lever? That might make noise if it was dry.)

Try adjusting the clutch with just a hair more free play between the slave piston and the clutch lever.
(the pressure plate fingers are probably barely brushing against the throw out bearing; the guy in the video is pushing the clutch lever back on to the slave piston which would move the throw out bearing away from the pressure plate)

Note: if the same noise occurs when you engage the clutch, your throw out bearing could be going bad.

take care,
ChrisS