To approach the question scientifically, the first step would be to group things into Chess and NotChess. Then we find the common features of the Chess group to come up with a first approximation. Later, refinement of the answer might lead us to remove something from the initial list. For example, I remember learning in school that a Panda was not a bear, but a cousin of the raccoon. That’s not the view today.
I tend to take a very broad view, and consider all these things as Chess:
Go (Weiqi)
Chinese Chess (Xiangqi)
Western Chess (Chess)
Japanese Chess (Shogi)
Checkers (Draughts)
Gomoku
Tic-Tac-Toe
Since I include Tic-Tac-Toe in the list, there would obviously be many other things that I would include. These are just the ones that I could list off the top of my head. To make the list non-controversial (!) I picked only board games.
Here is what I find they have in common:
Two player.
Zero sum.
Turn-based.
Finite.
No random element in the turn.
Abstract positional objective.
That last one is interesting. Maybe it’s just my own delusion. Go definitely has an abstract positional objective (control of space), as does Tic-Tac-Toe. At first I wanted to say that Checkers does not (and thus remove it from the list), because the primary objective, capture of all the enemy men, is not abstract at all but just an extension of the capture of a single man. Well, the same argument could apply to Western Chess, that checkmate is a very weak abstraction of check. It would be puzzling indeed to say that Go and Tic-Tac-Toe are Chess, while Western Chess is NotChess. (I actually don’t know enough about Chinese or Japanese Chess to say where they fit here. As I said, this list was off the top of my head.) Upon further reflection, though, I think Checkers is saved by its second objective, taking away all the enemy’s moves. And I think Western Chess is saved by the notion of stalemate.
Suppose you (not me) consider that Tic-Tac-Toe, Gomoku and Go don’t belong in the Chess group, but are NotChess. Fine. Now you might add to the list of common elements:
Fixed starting array.
Adding Fischer-Random or 960 to the group might change the list again. Or maybe you consider it important that some of the Chess-pieces have different movements. And so on. Start with the broad features and make it more exact, until you have a pretty good working definition of Chess.
Anyway, all this is just preliminary to what I consider a much more interesting question. Why is Western Chess the best form of Chess? (You might pose the question differently: Why is Chess better than those other NotChess games?) I consider Western Chess best not because I like it best, which is probably just accidental, but because so many other people on the planet like it best. Which may also be accidental, but somehow I think not. The wisdom of crowds.