It seems I touched a nerve when I said that getting better at playing a zero-sum game isn't a good way to make the world a better place.
I was thinking of day-traders at the time; people who don't care what asset they're buying and selling but just try to buy low and sell high to make a profit. Or high-frequency traders who try to be just a tiny bit faster executing transactions to take advantage of tiny inefficiencies in markets.
Probably I don't have a deep enough understanding of the value of liquidity in asset markets or a deep enough appreciation for their role in creating market prices, but it seems to me the world would get along just fine without them spending all their time and effort competing against each other.
I wasn't thinking of competition in general as being a zero-sum game, because in general it is not. Competition drives efficiency, and efficiency (creating more by using less) is what makes the world a better place -- assuming that the thing you're making more efficient has a positive effect on the world. Competing to build the most efficient bomb or assault rifle is not a world-improving activity.
To bring it back to Bitcoin: competition between Bitcoin miners is a zero-sum game for the miners, but if you think that Bitcoin will make the world a better place (I do) then the competition to be more efficient at mining is a net positive for the world as a whole.