They can't be capturing photons in motion, or capturing anything "moving at the speed of light." That doesn't make any sense. According to relativity, photons don't actually "move" at all. (As I understand it.)
As plain English descriptions go, I think it's satisfactory. If you know enough to know what's really going on, the video still has plenty of information to describe what they are really doing. I rather suspect they already know that.
Also, photons don't "move" in their own reference frame, in which the entire universe is a zero-dimensional point with no time; for everybody who has mass, they are moving. At the risk of being mass-o-centric, I think it's not that wrong to speak of their "motion". Some of my best friends have mass.
Photons do in fact "move" by any reasonable definitions of the word. In fact, unlike massive objects, photons are moving in all inertial reference frames. They travel along "light-like" paths through spacetime:
