Um, no.
Familicide only kills beings linked by a *living* immediate family member (that's being generous, could just be Parent/Child).
While disastrous in the modern, highly intermarried context. It's much less damaging if you consider that for most of human history in most parts fo the world marriages were largely confined to members of a group/tribe/smaller region. Eventually there would be no living links.
It's an interesting sociological question what the linkage of modern humans is and how disastrous it would be, but it definitely wouldn't kill non-humans. There are no *living* blood relations among humans and non-humans. (This is kind of what defines "species" in the real world.)