I think the crash course video does a good job of giving a very minimal explanation of the Ramayana. They completely leave out some of the important aspects of this text as a religious text, which I think was something that needed to be included. There is not reason to why this is such a significant story or why it is still around today. There is also not a lot of history as to why and how this story came to be. There are some details in the story that this video tells that are the same from the version we read. This could be because of how many different versions there are of this story. One place I really noticed this was the way the video explained Rama being banished to the forest. There were a few details that weren't the same-- like why and how it all happened and for how long.
I don't think that "mythology" is the best way to explain this story. This makes it seem like this isn't as significant as other religious texts or that is just isn't true. I'm nit sure why this was used. My best guess is just that because people are unfamiliar with the text they are really sure how to characterize this text. I think that since we aren't in a culture that is saturated with this text it can be difficult for us to comprehend how important this text is. I think not calling it "mythology" would have helped the viewer understand this story a little bit better.