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IMHO, Muller's 7 criteria look quite useful for estimating how chess-like a game is--a continuum, rather than a binary is/isn't categorization. They would provide a conceptual framework for observations such as (to intentionally cite an extreme example) Capablanca's Chess is more chess-like than the Game of Nemeroth. Where the line is between chess variant and non-chess games cannot and indeed need not be determined exactly. The question is, is a given game chess-like enough for it to be useful to consider the game a chess variant--can a useful number of Chess concepts be helpful in playing and analyzing the game?

But drawing lines can be fun and useful if it isn't absolutized. Approached in a spirit of 'reasonable people can disagree', everyone should be free to chime in.

As a starting point for looking at some edge cases, I offer my own game Wizards' War for consideration: 
1. It has royal pieces, though capturing them is not the only method of victory.
2. It is entirely pawnless (in the Muller sense--many games are pawnless in the sense of 'this game has no piece that moves like an FIDE pawn').
So is it a chess variant or not and why? Bonus points for citing games that are clearly but not hugely more/less chess-like.