Erm, Sputnik was a military satellite. It was designed and launched by the soviet ministry of defence, using an ICBM.
Pretty much everything on both sides at that point in the space race wise was being done by the military, especially since it pre-dates the formation of NASA.
Also, it is a 2 year old video, so I'm unsure how good you're expecting his V2 replica to be when made using 1.35.