I'm not sure if we have a special term for "web-fiction" in Russian. I bet we'd just call that "fiction", which is фантастика in Russian, as no one would care that web fiction is a work of fiction available primarily or solely on the internet. It's genre or subgenre what matters to us, not where you can find a work of art. E.g. A web fiction written in science fiction genre would just be научная фантастика for us.

Cyber fiction is definitely a genre, so it is a thing in Russian - киберфантастика.

https://www.google.ru/search?q=what+...B8%D0%BA%D0%B0