Honestly a great question op, Id love to hear how the author describes it too. What I think is that we can call it fic bc fic is a mode of writing in as much as it is. Meaning its not just fiction written about existing media, fanfic is also a distinct form of writing from which recognizable styles, tropes and language has emerged.
This story in question, while all the characters are original, fits the mode of fic: the style, tropes, audience, and publication (ie: free and non professional) are recognizably "fanfic". It's much more similar to fanfic than it is to a regular published novel.