Take notice in your video at 0:02.
During his release, his glove comes up, just under his pitching shoulder. This is his way of supporting his shoulder exchange - glove shoulder being replaced by his pitching shoulder, which by the way looks pretty solid.
On the other hand, for a pitcher of his age - tall and slender, it's not all that unusual to see this posture. Now before you think that something is wrong, there's nothing wrong here. He has an excellent body flow of momentum and control. In fact, he senses that his pitching shoulder has to has some support, all because his strength and development upstairs in his upper body isn't there yet with the strength factors necessary to compliment his overall pitching style.
That "arm swing" thing that you mentioned is not all that unusual either for someone of his build and age. Again, once he puts a few more pounds on, a little more in the conditioning department, he'll do just fine. In that regard, trying to fix things that are age and maturity factors are something that are just out of his control right now. And on that note, be careful not to push him into a winning mode instead of a development mode. He'll continue to pitch the way he's doing now, only because he has a lot of maturing to go yet.
Video of him in two ways - first a side view and back view of him playing a simple game of catch, then another video of him from the back and then a video from the side of him pitching would be very helpful.