The MIT News Office article has more details than the PR video and a link to the paper: http://web.mit.edu/newsoffice/2011/trillion-fps-camera-1213....
The actual imaging device is just a long line of photosensors. The camera aperture uses a varying electric field to deflect photons that arrive later to sensors further down the line, producing an image in effective 2D - 1D of space and 1D of time. By repeating the scene and slowly scanning the camera's mirror, a composite video is built that shows diffusion of a picosecond laser pulse.