Non-Tolkienian

Elves can exist and not be Tolkienian if they follow more traditional elves rather than those presented by Tolkien.

Although Tolkienian fantasy generally is recognized most easily form the presence of dwarves and elves who hate/dislike each other, both are not required to exist in the setting nor the hate between those two peoples.

Presence of Orcs do not necessarily count, even if they were Tolkien's invention. But one can be fairly certain it's Tolkienian when at least two of these three demi-humans exist within the setting.