Is chess a zero sum game? "Chess is a zero sum game" is a claim you see often, even on this forum. 

Game theorists will tell you that it is just obvious. Either the game is a draw, nobody wins or loses, or one side wins and the other loses. A win is equal and opposite to a loss and a draw is worthless. QED.

Economic trade is a classic example of a non-zero sum game. In fact it is a win-win game. If that weren't the case then there would be no trade. Nobody would trade freely if they knew they were going to lose in advance.
When I said chess is a zero sum game in that answer, I wasn't referring to anything involving ratings. Obviously if we include ratings then chess isn't strictly a zero sum game, since the gains and losses aren't always balanced out. But different rating systems are arbitrary, and aren't part of the game of chess itself.

Your question should be "Is the FIDE rating system a zero sum game?"