Mining isn't a zero sum game.  It is a fixed positive sum game.  Maybe that is why you are confused.

A zero sum mining game would be that all miners need to put a certain amount of Bitcoins into escrow.  Once 25 BTC have been escrowed a satoshi is randomly selected and the miner who owns it gets the entire escrow amount.

Zero sum =/= Fixed Positive Sum.

At the current exchange rate the mining "game" has a positive sum of 25*6*24*365*~$100 = $131,400,000 annually.