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A friend of mine dedicated to playing chess once referred to chess variants as 'fantasy chess'. I thought he'd merely somewhat unjustifiably coined a phrase, but I got around to Googling the term, and here's Google's definition for 'meaning of fantasy chess':

Knightmare Chess is a fantasy chess variant published by Steve Jackson Games (SJG) in 1996. It is a translation of a French game Tempête sur l'échiquier (Storm on the Chessboard), designed by Pierre Cléquin and Bruno Faidutti.

So, Google is including the use of this, maybe an actually incorrect term, too? [edit: their use here is 'fantasy chess variant', if one ignores their bold-facing.]

Otherwise, I've read that, strictly speaking, the term fairy chess is reserved for fairy chess problems, though the term is often used to refer to chess variants instead.