When is a game not a chess 'variant'?

One of the occupational hazards of being on the FIDE Rules Commission, is that you occasionally get sent new variants of chess, which the author hopes will be adopted alongside the current version. Of course this is not going to happen (as FIDE just deals with a very narrow definition of chess), but it makes me wonder about what is acceptable as a chess variant.
Clearly checkers is not considered a form of chess, so the type and movement of pieces is important. Although 64 squares might seem obvious, you might say Transfer is played on 128 squares, but even if you consider that 2 distinct boards, there are variants that use larger boards. There os also the goal of the game, with most variants requiring you to checkmate (or sometimes capture) the King to win the game. Of course this does apply to a game like Suicide chess, and other games like 'One check' chess.
Ultimately I think that games that 'look' like chess seem to be chess 'like'. If we consider chess consists of a board (of a specified size and shape), pieces (which move in a chess defined manner), and a goal (checkmate or something else), then games which approximate these features probably count. But if this is the case, why is a game like 'Feudal' (which I played as a child), not within this realm?