This isn't anything new. They spin up the main rotor, disengage the engine, then increase the pitch to do a jump start. According to this article, the first autogyro to perform a jump takeoff was the Cierva C.30 Autogyro back in 1934. For landing, autogyros perform a very steep autorotation approach (pretty normal for autogyros) and can stop in no time at all. The biggest limitation of an autogyro is that it can't hover.

What makes the CarterCopter interesting is its speed. Due to some clever design, they believe the vehicle is capable of speeds over 400 MPH, over twice as fast as a helicopter. The mechanisms for autogyros are much simplier than helicopters, so they usually cost less and they're easier to fly.