This video tried to fit all of Valmiki's Ramayana into a 13-minute video, so it's natural that they would remove certain parts. I believe that it was a good attempt at providing an overview, but it should not be considered a scholarly resource. I would recommend that this video be used for a brief overview of the work but it wouldn't be helpful for someone who is genuinely trying to understand the Ramayana in depth. There is information that is incredibly useful for someone trying to understand the family tree, but other than that everything is glossed over and you just get brief glimpses of what happens in the Ramayana.
I believe that this falls under the title of "mythology" since it is being viewed from a cultural viewpoint versus a religious one. I don't believe that there is any harm in using the word "mythology" because the Ramayana is mythological in its nature. Christianity, of course, also has a lot of myths and there is no harm in acknowledging that something can be both a myth and a religious truth.