Just to add $.02: I think the basic answers to your question have been suggested, and just want to emphasize the time in which Rice started publishing. In the late 1970s, early 1980s, the horror novel ala Stephen King and Peter Straub was making waves and her work, at least superficially, was part of that wave. King, Rice and Dean Koontz were so popular they weren't just genre anymore (even though they helped establish the commercial genre of horror), they were best-sellers. Even when the horror-boom burst, they continued on as bankable writers; Straub, too, though to a lesser degree.
There were other writers at that time and later who were working vampires from different angles -- Les Daniels, Suzie McKee Charnas, Chelsea Quinn Yarbro, Poppy Z. Brite all come to mind -- and I don't think any of their vampire works have been adopted by the fantasy crowd, either. Most of that generation of horror writer hasn't been drawn into fantasy, I don't think. Tanith Lee is something of an exception, but that may be because most of her work slides across the (rather permeable) borders of s.f., fantasy and horror and early on she established herself as a fantasy writer with non-vampire, more Sword & Sorcery type work. Also Kim Newman, whose Anno Dracula is something of a precursor to the fantasies set in Victorian times that have appeared in the last decade or so, and so an alternate history vampire novel.
For what it's worth, I think the majority of horror falls into either fantasy, s.f. or mystery. I think the degree to which the fantasy element is developed -- as opposed, maybe, to the determination to frighten -- may determine whether other fantasy readers agree or not.
Randy M.