I presume you're referring to the ring-flash, mounted on/around the lens? It's primary purpose will have been to create that harsh light on the centre of BC's face, without excessively lighting the background. Can't say from what's shown in the video, but the ring flash may also be triggering other flashes (e.g. whatever lights are responsible for the reflected highlights on the lightbulbs and shiny knobs on the set).
Although it's common to think of flashes creating the kind of harsh shadows you see in family snapshots, that's really only an effect of using a single flash in a lighting arrangement - mainly because none of your family want to waste party time while you spend six hours setting up the additional lighting! But whereas a movie crew fires up a collection of megawatts and floods the set for as long as it takes to shoot the scene, a portrait photographer only needs that kind of light for a fraction of a second.
You can rig up a whole set of auxillary lights, each with their own adjustable output, and fit each one with an optical slave that fires when the main flash fires. That gives you the intensity of light needed for a high shutter speed and fast film, but only for that fraction of a second - much more comfortable for the subject to work with. In this case, it's probably more important than for an average photoshoot, as the photographer would have wanted a good depth of field to keep all that foreground and background detail in focus as well as the subject.