It's a funny thing history. Fairly recently I was watching a YouTube video about how what we *think* we know of history can be deceptive because when they teach it to you in schools they have to pick and choose what to cover for lessons and so they streamline historical events into simpler narratives to make them easier to understand and remember. But history is of course rarely so simple.
I was reminded of that video when playing "
Ghost of Tsushima" and watching the TV anime "
Angolmois" back to back and it's interesting because they both depict the Mongol invasion of Tsushima but very differently so, mainly because of the mediums involved. Particularly in GoT's case as it is a video game with tens of hours of gameplay they probably felt they needed to keep the story simpler so you didn't forget what was going on. An easy to explain change would be the forces of the Mongol Empire in GoT appear to consist exclusively of Mongolians whereas in reality they were a hodgepodge of Mongolian, Chinese, Jurchen and Korean all having to work together despite differences in language and culture.
Not a knock against either series really, just an observation. Though maybe don't use fiction as your source when writing essays on history.