While I do find fight scenes like those Jacki directs visually pleasing and easy to follow, I think that his and American-directed fight scenes are trying to achieve different things. Like the video said, Jackie is oftentimes trying to fuse aspects of comedy with the fights, and he does it well. Comedy tends to be easy to see and understand, lacking in significant franticness and desperation. Additionally, he is a true martial artist. He's trying to convey a sense of amazing talent in his fights.
Few American movies lately (as far as I can recall) try to claim martial arts mastery, or really any sort of truly notable skill. The actors who portray fighters in those scenes tend to be just actors, not martial artists. They don't have the sheer aptitude to pull off what Jackie does.
In any case, American action movies generally aren't comedies. They try to be edgy and brutal. Camera shake does serve a purpose of insinuating desperation; like the fight is truly to the death. In very rare cases is one going to encounter a skilled martial artist during a fight scene, so there isn't much room for flashiness or kookie moves. These people are literally trying to kill each other, which (in the real world) generally means they are pretty much struggling on one another.
I think Jackie's fight scenes do well in conveying a sense of experience; you're watching a martial artist do what he has trained his life to do.
American action scenes do well to convey desperation; you're watching individuals try to kill one another as fast as they can, which tends not to be pretty.