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Although I regard Muller's list of seven desirable conditions as an excellent guideline (on most points, in my opinion) for being conducive to the possibly of creating a high-quality chess variant (which is pertinent to the title of this thread), the present question as to what defines a chess variant yields fewer conditions.

Generally, if a game has a board (2-D or 3-D) with spaces (e.g., square, 
triangular or hexagonal in 2-D), some (not necessarily all) mobile pieces
that occupy those spaces, a turn-based move order [Note:  I've never been able to successfully devise a simultaneous move game.] implying two or more players and a winning condition, it is a chess variant.  Even capturing (by various means) is not mandatory to this definition.  Also, having different piece types and abundances is not mandatory although both are strongly advisable since a lack of variety diminishes tactical depth.

So, chess variants actually include many classes of games that are not popularly classified as such.  For example:  connection games, war games, checkers variants, shogi variants, ultima variants, etc.  Furthermore, the hybrid usage of dice, cards, etc to render the overall game one of imperfect information is not prohibited.