I came across this GIF and found out it is a Krieghoff Semprio. The Semprio is an In-Line action system that functions like a pump-action rifle. However Krieghoff desgined it differently.

Quick target acquisition in close quarters – just one of many hunting situations where the Krieghoff In-Line action proves its superiority. Lightning fast reloading and repeat firing without changing hand position – a true speed advantage of the Semprio. Hunting is now what it should be – a total focus on the target and safe shooting without distraction. Ergonomic repeating naturally draws the rifle into the shoulder further enhancing high shooting accuracy.
To repeat, the entire barrel in-line assembly is simply pushed forward with the guiding hand. Thereby the gun will be unlocked, the empty cartridge is ejected and the next round will be fed from the magazine. Pulling back the entire barrel in-line assembly shuts and locks the rifle and readies it for immediate firing. During the entire firing sequence, the hand positions never change. All precision parts of the mechanically operating In-Line action are moving on polished, friction-free sliders. The Semprio is designed to accommodate both right and lefthanded shooters.
The steel bolt head with seven solid lugs rotates and locks in the barrel assembly. The broad 65 mm² (0.101 square inch) locking surface offers the highest level of confidence and safety. The trigger can only be pulled when the rifle is completely closed and locked. The In-Line action rifle can be easily loaded through the large ejection port or by quickly changing the detachable magazine

The Krieghoff In-Line action is quite different from what many of us are accustomed to in a pump action rifle. In a traditional pump action, the fore grip is pulled back to cycle the bolt and extract the spent casing. The Krieghoff is different in that the entire barrel assembly is fixed with the fore grip and the entire barrel assembly is pushed forward away from the fixed bolt to extract the round and then pulled back together to chamber the round.

In The GIF above and video below, the shooter is not working the action properly. The shooter is supposed to push the barrel forward while leaving the stock shouldered and maintaining his cheek weld.

According to a review by Craig Boddington, the Semprio In-Line action allows it to change calibers easily.

Here are the specs off Krieghoff’s website.

Standard caliber: .223 Rem., .243 Win., 6,5×55 SE, .270 Win., 7×64, .308 Win., .30–06, 8x57IS, 9,3×62

Magazine capacity standard caliber: 4+1 – 4 rounds and one extra in barrel

Magnum caliber: 7mm Rem. Mag., .300 Win. Mag., .375 Ruger*

Magazine capacity standard caliber: 3+1 – 3 rounds and one extra in barrel

Standard barrel length:
55 cm (22″) for standard caliber
63 cm (25″) for magnum caliber

Direct triggering: approx. 1.25 kg

Weight**: approx. 3.4 kg

An added benefit to the design is that it is a takedown rifle.