Indeed, the question given in the title does not make sense without the prior definition of what is a "board game", and the latter appears to be quite arbitrary and unsatisfying whatever restriction(s) would be chosen. To motivate this opinion, consider that even the most "basic" requirements given in earlier answers are unsatisfying: (1) The finite number of possible constellations: as mentioned somewhere, one could well imagine pieces which grow in (whatever) "strength" without limit (one can imagine a kind of "promotion" that allows a player to "attach" an arbitrarily large number to any of his pieces). (2) A move = piece taken from one location to another, possibly removing another enemy piece: obviously, an arbitrary number of enemy pieces might be removed (as in Go). Also, to include moves similar to castling in chess, the definition must potentially allow several pieces from different locations to move at once into possibly any other location. To include promotions, pieces must be able to be changed into any other of the (as said earlier, possibly infinitely many) pieces. Also, many board games involve throwing dice (which was the case for chess in medieval times), asking and answering questions to the other player, .... So, in short, it appears that any imaginable transition from one "state" of the "board" (comprising much more than the finite number  of locations, infinite number of possible pieces, and other accessories like dice, clocks, infinite collections of questions and answers ...) to virtually any other state of the board, must be compatible with a general definition. We see that the physical board and the "currently active pieces placed on that board" are only an infinitesimal part of a possible "state". So, whatever restriction could prevent *any* game of being a board game, according to any satisfyingly general definition of the latter, which should encompass at least all of the well known classical board games? We should admit that on a closer look, the "board" itself is an (almost(?)) negligible part of many board games. And any non board game would actually be a board game with a possibly trivial (empty or singleton) set of "locations".