I pretty much agree with most of the posters here.
When people refer to "classic" fantasy, what they really mean often is Tolkien fantasy. Tolkien was hugely successful and spawned a ton of imitators, especially in the 80's and 90's. But for as long as there has been Tolkien-esq fantasy, there have been people using strange races in their works, or incorporating "lost" sci-fi technology into there narrative, or people who use talking animal folk. Hell most of the tropes actually predate The Hobbit.
If anything, you could make a solid argument that "classic fantasy (e.g. what you see in Conan as well as many other settings)" really is about very low magic and no other significant races, and those other races that are around are rare NPCS or monsters to be slain. Pathfinder and DnD certainly don't fit within that definition.