To elaborate on what i think Christoffer is saying, and adding some of my POV using my ~10 years different types of tactical shooting...
when your head bumps around the aiming dot will stay close to where the bullet will impact at it's zeroed range, so it will move around but only relative to how much your head moves relative to your rifle. So a tactical shooter with some trigger-time or a trained operator will have eliminated most of that head/dot movement. Rifle sway/bumping while walking on the other hand is a lot harder to minimize and take a LOT of training to minimize and some sway will always be there whenever your heel hits the ground. it is something you have to learn to shot with, timing the shoots so you shoot while you are most stable. This is especially important with a rifle that recoil harder. so Staying on target while walking is hella hard.
Btw the vid you posted is a reflex sight and not a holographic sight, they might look the same but are a lot different when you use them in the field since holographic sights create a superimposed image at a distance of the field of view. To put it in layman's terms, it looks like the dot is ON the target 100 or so meters in front of you and not just a dot reflected on a plain of glass.
The only thing that vid shows is the problem with Parallax in cheaper optics.
Actually it will not, the further the dot are from the center of the optic the more distorted the aiming reticle will be it is more noticeable on cheaper optics like Pilad and especially some china replicas. In addition to this you do have Parallax "a displacement or difference in the apparent position of an object viewed along two different lines of sight". But high grade red-dots and Holographic sights got different tech to compensate for this so it is just about not an issue.
If you wonder what Parallax looks like in a cheaper optic just look at Christoffer5700's vid at the start of this thread and notice how the dot shifts in relation to what it is aimed when he moves the camera
sorry for the long txt and it might me nitpicking, but for a guy with some time in the field it is important details
Edit: i realize now that some of this might be hard to implement in a game. (but, i am no game developer)