I am in no way qualified to answer this as I am not in the military or have had any sort of training, but have shot a few guns including AR-15's in my short life. You are correct in assuming that the .223 or 5.56 round has much less recoil than a hunting rifle (which I've also shot plenty of) but I don't think this is the reason they are doing it. The left leg or right leg forward approach is much more stable than standing like this, but I believe they are doing this so they can train both ways ambidextrously and also to train for quick situations when they can't get a steady firing position before shooting. Being unsteady like this also helps them build their stability better and not rely on perfect situation stability for high-stress and fast paced situation. I imagine that when they take their marksmen test they will use the more stable position but otherwise will use the more versatile position like so.

And for your other question of leaning a bit forward this is also standard practice for the stable standing position and I prefer it too, but when I was firing the .223 caliber AR-15 there was very little kick. Since I was using the stable standing position that my hunter safety course taught me, the AR-15 did not kick much and I became unstable after a few rounds because as I leaned forward I started to drift further and further downward. I understand that this straight on position demonstrated in the gfy might be more stable for small caliber rifles but I don't have enough experience to make a good observation.

Oh and since I don't feel like implementing this into the top AR-15's are nothing like a hunting rifle when holding it. The first time I held one I realized they were quite small compared to even my .243 that I usually hunt with. They are much more compact for more stability and you can hold it quite close to your body to keep steady, something you can't do with a hunting rifle. This stance demonstrated in the gfy is very unstable for a hunting rifle but would be much better with a small compact AR-15.

Of course my opinion is no where in comparison to someone who's had experience with M4's in the military which it looks like the soldiers in the gfy. An AR-15 is quite similar in size and feel though and I have shot them a few times so take this writing with a grain of salt. I hope someone more experienced can answer this question for you!