It is zero sum because it adjusts, no matter what you do. If you pump more oil from the ground, the prices will fluctuate until they reach the new zero-sum level that takes into account the new production level.
A pegged dollar is the same, it only takes a little longer. When they print they dilute the value of the current dollars in circulation but not immediately, because of the peg. But eventually, because it is zero-sum, so much pressure is pent-up trying to maintain that non-zero-sum peg that the system begins to crack and they have to re-peg it. Which happens often with pegged currencies.
This does not mean there are no winners and losers, personal finance is of course not a zero-sum game. And because the adjustments are not instantaneous there is a lot of room to profit if you know what is happening, which gives the impression of it not being zero-sum.
