The single defining quality of 'Chess' is that
the winning condition is predicated on one (the royal) of two (royal and non-royal) classes of pieces
If this statement is accepted then for a game to be a chess variant it must have these 2 rules: one to define the royal and non-royal classes; and one to define the winning condition in terms of the royal class.
... what fixed set of rules would be needed to still identify the game as chess, and allow for infinite variations? ...
From the CVwiki we have
The single defining quality of 'Chess' is that
the winning condition is predicated on one (the royal) of two (royal and non-royal) classes of pieces
If this statement is accepted then for a game to be a chess variant it must have these 2 rules: one to define the royal and non-royal classes; and one to define the winning condition in terms of the royal class.