Ah! You watched the video. Interesting, what?
Read the next few paragraphs carefully.
Going by the response that you deleted...and I'm not tryin' to bust your chops here...just tryin' to educate you a little.
I know that the barrel and slide move backwards together, that is why it's not possible for the gas pressure pushing on the breech face to be the force pushing the slide and barrel backwards.
Why do you feel like the gas pressure/force can't push the slide backward? Again...It's the only force in the system. There is no other force in the system. While the slide and barrel are connected, they're essentially one mass. Think of it as a variable mass breechblock that "loses weight" when the barrel is disconnected. Here, it operates no differently than a straight blowback...except while the bullet is present...it's frictional resistance in the barrel is acting as a delaying mechanism...resisting the barrel's rearward move, and thus the slide's.
The bullet is moving forward...which means that the barrel can move backward. Because the slide is being driven backward by the force created by gas pressure...and because the lugs mechanically connect it to the barrel...the barrel moves along with the slide.
Grasp a broomhandle in front of you in both hands. Pull hard in opposite directions. Just when you're exerting a good amount of force...loosen the grip on the handle with one hand just enough to let it slip. When the handle starts to slip through your hand...your hand starts to slip on the handle. Now you have an action and a reaction. Before the slip....you had equilibrium from the balanced forces.
The broomhandle is the bullet. The slipping hand is the barrel. The wrist on the slipping hand is the locking mechanism. The forearm is the slide.
No, it doesn't matter that the compelling force comes from the outside...pulling both objects instead of from the inside pushing them. The "bullet" and the "slide/barrel assembly" don't know where the force is coming from. They only know that a force is compelling them to move in their respective directions.
To recap:
Momentum isn't a force. Momentum doesn't cause things to move. Force causes things to move. Momentum keeps them moving. Refer to Newton 1B...to wit:
"An object in motion tends to remain in motion unless an outside force is imposed on that object."
Here, Newton was describing conservation of momentum.
Recoil isn't a force. Recoil is the result of a force applied, and the acceleration that it suffered because of that force. Recoil is acceleration. Recoil only occurs during acceleration. Once the accelerative force is removed, and further movement is accomplished via momentum.
Once the bullet exits the barrel, the force goes with it. Neither bullet nor slide is being compelled to accelerate. They continue to move because of the momentum that they conserved during their acceleration...while the system was active...and they are now compelled by outside forces that are trying to bring them to a stop.