Bitcoin is most certainly not zero sum. Zero Sum implies that for every winner, there must be a loser. It is quite possible for everyone to lose money on Bitcoin, with no winner.
If tomorrow the USA gets together with China and Russia and persuades the entire world to outlaw Bitcoin, with the threat of a heavy punishment for anyone trading in Bitcoin, the value of Bitcoin will crash, probably very close to 0. In this scenario (which is not all that far-fetched) absolutely everyone loses, hence not a zero sum market.
Each bitcoin-dollar transaction has a winner (not really a winner, but someone left holding dollars after a bitcoin crash). Given that, the vast majority of lost value would just be in the notional value of bitcoin.
If you and I agree that we each own a million fake dollars, we don't actually lose anything when later we decide we aren't.
If tomorrow the USA gets together with China and Russia and persuades the entire world to outlaw Bitcoin, with the threat of a heavy punishment for anyone trading in Bitcoin, the value of Bitcoin will crash, probably very close to 0. In this scenario (which is not all that far-fetched) absolutely everyone loses, hence not a zero sum market.