As far as I can tell from the story, the camera works by shooting light into an electric field, which makes the light bounce off -- and one of the directions in which it bounces is towards the camera. The camera is then shifted downrange for the next shot and the next, and so on, until it captures images from the light all the way through the bottle.
The only reason this works is because the light is being sent along the same path every time, so the conditions can be replicated each time. According to the scientists who built the camera, it's working at what would be roughly a trillion frames a second. You'd think it would take forever to make the shot then, but the light takes only a tiny fraction of a second to reach the next place where the camera takes its picture so they finished in a little over an hour. Computers then stitched the images together to make a continuous video.
You might also scratch your head at the headline of the story's reference to light particles. Wait, you might have thought -- isn't light made up of waves? When did it come to be made up of particles?
Welcome, O fellow confused traveler, to the concept of complementarity, in which light behaves like a wave when it is measured by experiments that treat it like a wave, but like particles (photons, to be precise) when measured by experiments designed to treat it like it's made up of particles. But waves and particles are different things. Indeed. In essence, light is both of those things at once until you measure it, when it becomes the thing you measure for.
Physicist John Polkinghorne, also a retired Anglican priest and one of my favorite science writers, has said that this "wave-particle duality" only seems like a contradiction when we speak about it in words. The equations that physicists use to describe it eliminate the contradiction and make it clear how something can be both a wave and a particle at the same time.
But unfortunately, ever since a horrible accident in the seventh grade when some irresponsible teacher put letters and numbers up on the board in the same math problem I have been unable to speak Equation. So I take Rev. Dr. Polkinghorne's word for that.