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I suspect there's several concepts concealed in J�rg's [23].

One could be that squares differ only by their relative positions; for example, there's no square where you become immune to capture, or that can only be crossed by certain piece types, or whose occupation immediately wins the game.  Though this would be violated not only by the river and palace in Xiangqi, but also by piece promotion in FIDE and Shogi, which perhaps calls into question the validity of that criterion.

On the other hand, you can still make many kinds of 'terrain' just by altering the connections between squares; for example, you could have a 'wall' between squares (causing them to not be considered adjacent), or a 'portal' (that causes two otherwise distant squares to be considered adjacent), or a 'rotated' square (that turns forward movement into backwards movement, or orthogonal into diagonal, for example), all of which can be completely described purely as changes to the connections between squares.

So perhaps you want a rule something like 'the squares comprise a regular tesselation of the playing field'.

And possibly another requirement specifying the overall shape of the playing field (e.g. rectangular).

Side-Topics:
 - Chess variants on boards with semi-regular tesselations
 - Chess variants played on an arbitrary graph