Taking the rifle and bullet as one system, the total momentum just before the shot was zero. By principle of conservation of momentum, the total momentum just after the shot was fired should also be zero. Since the bullet carries a forward momentum, the rifle must recoil in the opposite momentum in order for the total momentum to remain zero.
Do note that the momentum of the bullet and rifle are exactly the same magnitude. So the ratio of the bullet and recoil velocity is the reciprocal of the ratio of their masses.
The rifle in use in this video is supposedly a 0.700 Nitro Express, which apparently uses an extraordinarily massive bullet. This exerbates the recoil which caught many subjects in the video by surprise.
xmDemo 
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