A succinct answer and basically correct.
My understanding of this is the clever part is the very short pulsed laser combined with a very short exposure camera. Each laser pulse send lots of photons together in a bunch across the field of view of the camera. Some clever camera synchronisation allows each "frame" taken by the camera to be slightly (pico seconds) later than the previous one. When run as a movie, this appears to show a light pulse as moves across the field of view.
However, it doesn't take a picture of a single photon - it takes pictures of a bunch of photons and neither does it take a movie of the same bunch of photons moving across the field of view - each frame is taken of a different laser pulse.
(for simplicity I've ignored the fact that the camera is a line scan camera rather than full frame camera)