3 Commando Brigade

Jetrise, actually it does not.  Rounds have very little inertia, nowhere near enough to knock a person off their feet.  You've watched too many movies.

Also that AI in RL would be so pumped full of adrenaline he'd unlikely feel the effects for several seconds, by which time one or both of them would be dead

Regardless of this movies vs realism debate, the armour values for the RHS Russian vests are part of their pack. If people feel they are too powerful, you need to be leaving feedback on their BIS thread / posting a bug report.

In real life, while a round hitting you in the chest won't have enough inertia to knock you down, I bet the reflex reaction (duck/crumble into a ball) from the shock of the impact and the severe bruising would be enough to render you ineffective after the first shot, at least for a while.

So I agree that the AI response is not realistic when wearing the RHS Russian vests, but game engine limitations are in play. Personally for game balance I'd rather RHS reduced the vest armour values a little bit.

However, now consider all the benefits that you human players have over the AI, and think about how unfair the AI must feel the game is! Adapt and overcome.

https://youtu.be/tMMSA3opBk4?t=50s

The question is what kind of armor this actually is. This might be something that is used for the personal protection of VIP's and not so much something for combat troops. 

That shows it very well Warren.

The momentum of the bullet strike (bullet mass x velocity) is comparatively small and doesn't knock him backwards.
But he falls down primarily because of the psychological effect of being hit, from which he recovers shortly afterwards when getting back on his feet. If he had been expecting the strike and was prepared, knowing that it wouldn't kill him, as in Dwayne's video, then he probably could have remained standing.

This is missing from ArmA game play with AI. There may be some suppression factors to make them take cover, but there's nothing to make them ragdoll/recover or reduce their aiming ability when they get hit. 

There definitely is a mechanism that causes the player to ragdoll when hit by a vehicle at low speed, then get back up (I'm not sure whether this comes from ACE or Vanilla or another mod). But either way, could this be something we could tap into?

As Apollo says its just the psychological shock, which very much depends on the situation.  The soldier on guard duty is not expecting to be shot, hence the surprise.

However, if two combatants come face to face (say in cqb) and each fire, both are expecting to be hit and it just becomes luck and instinct.  In which case fight or fight takes over.  It is not uncommon for soldiers to be seriously/critically  wounded and not realize, until that shot of adrenaline wears off, a few seconds after the fire fight concludes.

It's analogous to being in a bar fight.  You don't feel the pain until later

It's not just the psychological shock. The soldier describes how he felt like he'd been hit with a sledgehammer.

I guess we're all on the same page, agreeing that while the Russian should survive the 5.56mm shots to the vest, what isn't 'fair' is his (AI) ability to feel no ill effect from a magazine worth (30) of sledgehammer blows and be able to kill the player with extreme accuracy as if nothing had happened. While it's reasonable to argue that adrenaline may allow a combatant to remain standing (ignoring the pain), it makes fine muscle control (such as aiming) MUCH worse, so his accuracy should be all over the place.

Agreed on this last point, but that is already modeled into the AI, to some extent.  Their ability to perform is already reduced with suppression and damage.

I was reading an interesting thread on Discord by the AI programmers, re the problems with AI in A3.  One significant issue currently, is that they seem far too likely to go prone and return fire, to the detriment of anything else.  Which is why we have so much trouble in getting them to close with players.