Going by the second phrasing of the definition, though, genuineness and authenticity, in no way forces RL realism. Genuineness and authenticity could be in reference to the Fantasy genre, itself, or to archetypes within it, examples of it like specific works, and their settings, and so forth.
You could, of course, still get completely arbitrary. Define your own setting, and the things you place in it are, by definition, genuine and authentic to the settings, and the things you exclude are not.
I've been tempted to try having alternate science that used to be believed in our world. What if the emission theory of vision was true and some people could feel when they were looked at? What if vermin did spontaneously generate in trash heaps? Etc...