I think most of you are misunderstanding the video... that, or I am.

If I understand things correctly, this camera (array) can only effectively photograph physically unchanging scenes, because it does so over a period of time. The guy explaining it mentioned an array of 500 cameras, but more importantly, he showed how the camera captures a one-dimensional "scan-line" of the scene each time, necessitating the rotation of the mirror slightly after every exposure in order to capture the entire scene.
Combine all that with their laser that sends short pulses of light, and what you have is a camera that simply captures one "scan-line" of each laser pulse. Send 1080 laser pulses with the mirror angle adjusted between each one, and you have a single full-HD frame of a laser pulse. Repeat
that 30 times, with the timing between the laser pulse and the camera's exposure lengthened each time, and you have a 1-second-long full-HD "video" of a laser pulse.
In short, it's not a hi-speed camera per se - it's an incredible combination of exact repeatability, very precise camera-laser syncronization, and mirror control.
Note: I'm not sure where the array of 500 cameras comes in... possibly they're chained together to all take exposures of the same scene over the course of 500 nanoseconds (or whatever), resulting in a 16.66667 second (500/30) video of a single "scan-line". Repeat 1080 times for full HD.