it's a zero-sum game regardless.
say bitcoin were a closed system. no more fiat influx, constant market cap. any gains any trader makes will be another traders' loss. someone selling coins they bought for $5 last summer for $27 picks $22 out of every pocket which bought coins at higher prices.
however -- and this is niko's point as well -- since the market cap is small compared to the potential market cap, there is an influx of fiat which might allow for huge amounts of deflation on the long term which means anyone holding btc now who is still holding btc then will get a really, really good return on that investment.
but even in this case, everyone will not become rich. if you mean everyone who has btc now, then sure, but that's a pitifully small number compared to the amount of people and fiat required to really blow the price that high, and the last ones to 'convert to bitcoin' will be the ones whose money we're taking.
A bought one BTC from B for $2, and B bought back the coin for $4, and A bought it back again for $8, and B bought it back again for $16 ... Each time they made 100% return and both of them become rich in the process. The people who holding the BTC feel he is rich since the BTC price is high and he can sell it even higher later, and the people just profited from the trade also become rich and he want to buy again to enjoy the next ride
You might notice that there is only one BTC at any time and they just exchange it for more and more fiat at each trade. So how long the price appreciation will last depends on how much fiat they can put in the trade, before they exhausted most of their fiat reserve, the process will continue
And in current debt driven monetary system, fiat must increase exponentially to support it from collapsing, banks are getting fresh fiat money all the time and there will be people borrow these money to buy coins. Actually these people will become very important customers for banks, because in a mature economy, there will be less company who are willing to borrow