Okinawan Shito-Ryu Karate originated some 50-60 years ago as a form of combat and self defense, and while it's been tuned and toned down into what it is today (even the traditional Shito-Ryu style), it's always been fairly regimented and, well, very Japanese. However, the practice, self-discipline, so on and so forth can be found in many other sports - boxing for example. This doesn't change the fact that it originated as a way of defending yourself, and killing your opponent. Boxers punch punching bags, and Karateka perform kata. I don't differentiate, personally.
That being said, ONLY oriental fighting styles can be called martial arts, by simple definition of the word. Seriously, look it up. Martial arts are traditional oriental self defense forms. Otherwise, Fencing and all the rest would be considered martial arts.
That means that what that video shows is not, in fact, a martial art, regardless of what you've been told. That also means also that Capoeira isn't a martial art, along with, you guessed it, Parkour (I hope we can agree, at least, that Parkour isn't a martical art).
I thought it was pretty good though. All about disabling your opponant and kicking his ass as fast as possible. A lot of military fellows get training like that.