The narrative of the clip does not state the galaxies are moving through space at faster than the speed of light, Baz.
The narrative, quite explicitly, states "that these galaxies, whilst standing absolutely still, are racing away from us, in some cases, faster than the speed of light". The narrator then goes on to further qualify that statement by continuing "The space-time grows every larger by the minute".
So the reason for this apparent regression at greater than the speed of light is not because of the movement of the galaxies through the vacuum of space, but all because of the expansion of space-time.