Not denying that what this guy has done is impressive. However, it's simply a form of trick shooting. Any claims to historical accuracy is highly suspect by virtue of the claim that this style is a 'forgotten' style - meaning, there is no way to verify the accuracy beyond the guy's claim and is not supported by primary sources of the era. The claim that drawings from the era depict half-drawn bows is proof doesn't work since if those drawings are completely accurate and reliable, they would have included having the archer hold arrows in his hand much like Mr Andersen.
Moreover, the idea that archery was "forgotten" for a period of time is also untrue. For starters, Mongols and various other nomadic tribes have continued using bows as part of their daily lives uninterrupted for centuries. In addition, there are records of the use of the bow as a weapon in warfare as late as World War II.
Lastly, the effectiveness of this arrow-in-the-hand technique in actual warfare is also questionable. For starters, the touted high rate of fire. Sure, he can shoot those ten or so arrows pretty quickly. But what happens once he runs out? The position of the arrows in his shooting hand looks very cumbersome and appear like they may require time to be positioned correctly. Meaning, any time saved by this technique could potentially be lost while reloading.
Moreover, how long can he sustain that rate of fire? Battles last hours. Would he be able to shoot like that continuously for that long? The main limiting factor for an archer's rate of fire were the number of arrows supplied to him and his muscles tiring out.
Lastly, the distance he shot - with the target in front of him and the arrow flying directly at it in a close to straight line -is pitiful compared to the actual distances medieval archers had to shoot. Remember, archers were placed behind the cavalry and swordsmen. Meaning, the archer has to shoot past the rest of the army in front of him, the gap between the two armies and into the enemy's army. Alternatively, they would be trying to flank the enemy forces and sniping at them from the surrounding hills. Either way, the range required is much, much longer than what he obtained.