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This topic has been thrashed out before, most recently that I remember
here:
http://chessvariants.wikidot.com/forum/t-7708/chess-variants

The most complete answer was given by David Howe. I reproduce the key part
here, and recommend those interested to look at the wiki. It has far more
on this topic in various places.

 The 'Chess' family of games
DavidHoweDavidHowe 17 Apr 2007, 13:04 -0-400

What is the nature of the game of chess, and what makes a game a chess
variant? Here is my opinion:

'Chess', in the widest sense (ie. in the sense of a family of games),
has certain properties:

1. ...
9. It is a game that involves two classes of pieces, 'royal' and
'non-royal'. The winning condition of the game is to capture or
checkmate one or more of the royal pieces.

It is interesting to note, that the game of checkers, has the same [9]
properties, except for the last. I believe it is this last property that
differentiates chess from other non-chess games (such as checkers). ...