I've seen this video around a fair bit, but I can't find much background about who / what organization / style it is?
The video is from the World Martial Arts Association which was setup by Michael T. Dealy in the early 1990s, Mike Dealy trained under Grandmaster Duk Sung Son. The style is Chung Do Kwan, a form of Tae Kwon Do with light or no-contact.
The WMAA has a video channel on Youtube, but about a year ago all video's were removed, probably because of the criticism they received. The WMAA is often ridiculed on the Internet as being a McDojo/McDojang (for example see here, here and here)