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I agree that we should look for a continuum; probably the best approach is to decide upon several factors (like the Muller 7) that can be reasonably easily computed for different games.  What is perhaps lacking from the Muller7 is a measure for which aspects are most important (perhaps it is just equally weighted, but I think they should not be).  The ultimate goal (IMO) is for the measurements to come as close as possible to our collective opinion of what is 'chesslike'.  (See also Joyce's 'Chess Space', on the wikidot as well as in some comments here I believe.)

A couple of examples that might be helpful to keep in mind:
1) games using chess pieces that are not chesslike in gameplay: Joust (not very chesslike), or Knightsweeper (not chesslike at all) [both on this site]
2) Lennert's 'For the Crown' (half chess, half something else)
3) already mentioned, but Go and Checkers (and their variants; Gess perhaps?)
4) other games that are clearly not 'chesslike' but that have similarities should be noted; these might help weight the characteristics.

If 'chesslike' is not well defined enough, maybe it's useful to think in the following way.  If you wanted to tell a friend about this game, is it easier to say 'It's like chess, but...' or just to start from another game (or from nothing at all)?  Of course, some games will be equally easy to start from chess or to start from some other game (e.g., For the Crown seems easier to describe as 'like Dominion, but with chess', but maybe for some people, 'like chess, but with deck building' is better).

Oh, and maybe it's good to distinguish between a theoretical classification and guidelines for this site.  I tend to think this site should be very inclusive, but am happy to draw the boundaries tighter in theoretical talks.