Yes. I've seen the Lars Andersen archery video*. Everybody can stop sending me links to it now.
Speaking as a mediocre archer in my own right, and as somebody who's written three novels with a Mongol archer as a protagonist and done a fair amount of research on the subject of worldwide bow techniques...
That guy's a really good marketer.
But he's not actually doing anything we didn't already know about, he's not shooting in a manner that would be at all effective in combat or for the historically more common purpose of feeding his family, and his quiver-handling skills are worthy of the "before" segment of an infomercial.
I'd like to see him cut a sandwich with a regular knife! It might result in an explosion.
Here's the thing. He's basically misrepresenting a bunch of well-known techniques in non-Western-European archery as his own invention or "rediscovery" (bonus cultural appropriation!), and into the bargain, he's not actually putting any strength into that bow of his.
One of the things about archery is that arrows (even war and hunting arrows) are very light. E=MV^2, as we all know, right? So, if the mass of your projectile is slight, it needs to have a pretty good velocity to do some damage. Where that velocity comes from, in a bow, is the power. And where that power comes from is--surprise--your trapezius muscles.
Not your arms. And not actually the bow: the bow is a mechanical device that transforms back and shoulder strength into velocity, by means of storing the energy you use to draw it. It's more or less a simple mechanism that you spring-load with physical force, and then release. The more energy that bow is physically capable of storing, the more energy it takes to draw the bow.
This is what we mean when we say a bow has a "draw weight." I own two bows--a lightweight recurve, very simple and primitive, and a medium-weight compound bow, which are the ones with pulleys and stuff. (The pulleys are there to create a mechanical advantage, but they don't make it significantly easier to draw the bow. What they do is make it easier to hold the bow in a full draw. This is called letoff, and there's a bunch of technical stuff about round pulleys vs. oblong pulleys and you probably don't care about it anyway--and I don't understand it well enough to explain it even if you did. There are books, you can read some.)
Anyway. The reasons archers draw the way we do--which is to say, standing sideways to the target, less-dominant arm extended and slightly flexed with a relaxed wrist and loose grip on the bow; dominant hand brought back to the jaw or ear; dominant elbow raised and drawn back--is to engage the back muscles and create a broader draw. A significant portion of the power of your draw comes from those final inches, because of the way that springs work.
The thing he says about modern archers only drawing with one arm, by the way, is patent nonsense. Anybody who's had half an hour of archery instruction at a range populated by people who know what they're doing has been told to push the bow away with the bow hand as they simultaneously draw back with the draw hand.)
Also having a reliable anatomical point at which to anchor your draw, and a reliable stance, means that you have a reliable point of aim. Incredibly minor alterations in biomechanics--something as invisible as tensing your neck, or not fully broadening your back--can send an arrow wildly off course over distances as short as ten or twenty yards. Something as major as moving your draw point an inch? No freaking telling where that arrow is going.
When you are drawing a bow correctly, there is a feeling of being inside the span of the bow, a sense that the bow and your body have melded and that you are as much suspended in the tension of the bow as the bow is drawn by you.
Is this effective? Well, worldwide, millions--perhaps hundreds of millions!--of men and women successfully feed their families using this technique to this very day. They have cable channels up in the high digits where you can watch them do it. Whole cable channels devoted to stalking and killing deer and bear with a bow. Turkeys, too. Wild boar. Yes, it's effective.
Anyway, back to Mr. Andersen. His draw is likely to be largely useless for killing anything larger or farther away than a paper plate. It's any which way, and it's insufficient for power. (Also, hunting and war arrows are, generally speaking, much larger and heavier than what he's using there. E=MV^2, after all. Size does matter.)
Compare his release to that of Adama Swoboda (below), and see that Swoboda, even shooting fast, brings the bowstring back to his jaw. Andersen is shooting so fast that he doesn't have time for a full draw.
His tactics, though--speed shooting and so forth--are suited to a shorter recurve (like a Mongol, Hun, or Indian bow), which is designed to be shot in motion and from horseback.
If you're using a very heavy, penetrating bow such as an English/Welsh longbow, different tactics apply. For one thing, a heavier-limbed bow has a lot more mass, and accelerates the arrow in a different way. A laminated Mongol-style bow relies for its power on some gloriously advanced materials hacks involving laminating substances with different compressibility to one another and making them fight. They're snappy, and because they are small the tips of their limbs whip back into position speedily. You can't speed-fire a longbow that way, because the limbs of the bow are large, there's more mass to be moved, and they derive their draw power from compressing a quantity of wood. (They also make use of the varied compressibility of different substances, by the way--but those substances are the heartwood and sapwood of a young tree. Nature provides the lamination itself!)
(And massed fire with the things is indeed withering!)
And Mr. Andersen is firing so fast that he's not actually even getting his Asian-style bow to a full draw! He's basically doing the equivalent of swinging a hammer from the wrist; just plinking away, not really thumping on anything.
You can, in fact, fire these bows quite quickly. I've included some Youtube links to videos of people using them more correctly below. You'll notice that the master archers in those clips are handling their bows quite differently from Andersen. (He also has a death-clutch on the grip, which affects your aim rather badly. Proper grip on a bow is tender enough that when you loose the arrow, the bow actually rocks back against the web of your thumb.)
Meanwhile, to continue debunking his claims that modern archers don't use a right-side draw and that he's somehow reinvented the technique of keeping both eyes open:
If you look closely at the links below, you'll see that one of the Mongol/Hun techniques is indeed a right-side draw, and that a number of archers shoot with both eyes open. (This actually has more to do with whether you have a strongly dominant eye or not, in my experience, than the style of archery you prefer.) Another technique involves whipping the arrow from a quiver opening at your shoulder over your head, and not doing any of Andersen's dramatically inept banging it against the side of the bow. (Another infomercial moment.)
(I feel like Kirk in Wrath of Khan--"He's thinking in two dimensions!")
Andersen also neglects to mention (or possibly is not aware) that there are about seventeen different possible ways to grip a bowstring (not counting modern trigger or twist-style releases), and that one of the technical challenges of anyone who shoots a bow suitable for hunting or war is preventing nerve damage to the fingertips on the draw hand. Possibly because he's using a light bow and not drawing it to its full potential. The classically Asian/Mongol draw uses the thumb to hook the bowstring, with a flat-sided ring carved from animal horn to protect the thumb. (Tabs, archery rings, and so forth serve another purpose beside protecting the archer's fingers. They also provide a smooth surface for the string to slide off of, so that the friction of the archer's fingerprints snagging on her serving does not affect her aim. Yes, that's all it takes.)
You'll also notice that the traditional archers linked below have no problem keeping arrows in a quiver on a cantering horse!
Andersen's various trick shooting bits pretty much have to involve prepared materials. I feel like the Mythbusters have adequately debunked arrow splitting and arrow catching. (I myself have split a modern aluminum tube arrow on more than one occasion, which always makes you feel good but gets expensive.) The armor piercing trick is actually not particularly impressive. That looks to be costume chain, which is basically snipped bits of spring steel twisted together like a bunch of keychains. You can pull it apart with your hands.
And as for his shooting a guy across a table thing--I wouldn't try that with *gun*, frankly, let alone a bow. FBI guidelines for an officer armed with a firearm to safely kill an attacker armed with a knife are... 21 feet. Inside that range, and you are very likely to get cut.
*If you haven't seen it, there's an embed and an even eyerollinger response than mine over on Geek Dad. I saw a link to this post just as I was completing my own rant, or I'd probably have saved the time and just linked over there.
Here are some examples of similar rapid-fire and archery-in-motion techniques as used by modern archers, and a nice video of a military historian talking about some of the same things I have--and making some points of his own.