I own a DJI Phantom 2 Vision+.
I call it a drone. Or a quad copter. As you probably know, it does now have the capability of flying a preset path. So if the ability to fly a programmed path is your criteria, it qualifies. Another reason it qualifies is that it automatically maintains its position when I let go of the controls. That ability is on the flying machine itself. If the wind blows it off course, it will fly itself back to where it is supposed to be. Autonomously! Even when you're telling it where to go with your remote control, it's making a lot of the decisions of how to fight the wind and follow your instructions.
There are likely to be more updates to the firmware in the future that will allow it to do even more without a human at the stick. So it's best not to get too hung up on whether it qualifies as a drone, or whether it is "just" a lowly quadcopter.
Looking at the video, this is probably not the Phantom 2 with a gimbal and a Go Pro, nor is it the Phantom 2 Vision+. Possibly it's the Phantom 2 Vision, which doesn't have a gimbal to stabilize the video.