Part of the reason that guns are drawn in this case is due to the speed, which one poster said, and was correct by saying that it is considered criminal. Also, the windows were completely tinted, not able to see inside.
Although the officer drew his gun, it was mearly for his protection as he assesed the situation. He had the driver put both of his hands out the window, and open the door himself so that he did not have to get close (especially before back-up arrived). Once the other officer arrived, you notice that there was another person in the car (another reason guns being drawn because the first officer can only control one supspect at a time).
In this case, the officer did exactly as was trained. Based on the information given to him by the helicopter, he had to go into this interaction believing that this was a "criminal act" and thus he acted by pulling his gun out as a means of protection.
As for it taking so long to track the guy down...the helicopter was not going to let him get away. The only way they would be able to catch him, was if someone already ahead of him was available (you can't catch up to a 130mph from behind). The video was only like 10 minutes before he got off the highway, and once off the highway (where speeds were managable where police could catch up) it took less than a minute.
All in all, this is great police work when you truly look at it from all angles.