This style of driving is called "drifting" and while this video seems to have been shot in Japan, the concept of drifting is gaining increasing popularity in the US. Often, as a substitute for horsepower, drifters in the US put on bald or near-bald tires so as to reduce the traction tire-ground traction.
The type of drifting that is shown in the video requires a tremendous amount of driver control (its the most professional drifting that I've ever seen), since a little under- or over-drift can cause you to careen off the track.
Sweet video. Thanks for posting.
Regards.