Unfortunately I cannot access the video, but searching I found this one. Is it the same?

I think it is worth noting that the video does not portray the province as "so diverse". The video centers on a dark skinned boy and his father shows up at the end, there is no mention made of general demographics or the ethnic make up of the population at large. The only "claim" made by the video in this regard is that at one time, an officer of some rank was dark skinned. And that claim is trivially justifiable--there were plenty of people from the Middle East and Africa in Roman Britain, particularly in the military. There is an excellent little article at the Oxford University Press blog on this very topic focused on Hadrian's Wall. The Roman army should not really be called a "melting pot" (auxiliary units were nominally organized according to place of origin rather than all lumped together) but its makeup did represent the diversity of the empire.

So I am not really sure what the objections people have to this video are (well, technically I do know, I did glance over the video comments, but discussing that more specifically would require me to violate rule two and possibly rule one). The decision to portray the central character as dark skinned or light skinned would both be artistic ones, even if the latter is often considered "neutral". My suspicion is that consideration played heavily in the decision to have a dark skinned character.

There was a recent study of human remains buried in the fourth-century in the Roman British city of York. The study's goal was to figure out just how diverse the population was. The answer was, very--at least, for a backwater on the literal westernmost edge of civilization.

This article explains the study, which found that about 11-12% of the bodies they examined appeared to have had some African ancestry: https://www.ncbi.nlm.nih.gov/pubmed/19530143

This article (free to access) talks about one of these people, a woman who was born in North Africa and whose remains appear to be of a mixed African and European genetic heritage: http://centaur.reading.ac.uk/17041/1/M_Lewis_Bangle_Lady.pdf

Step outside York, and things in the British countryside would doubtless become much more white. Northern British countryside was not a place that anyone would want to willingly go, unless they had no choice, and the army along Hadrian's Wall was recruiting mostly from Germany at this time. That, however, reflects the backwater nature of the British countryside--if you went anywhere important in the empire (even big British cities like York) you would see some black and many brown faces. In some of the more important parts of the empire like Egypt, European faces would be the minority.