Adjusted to average growth of stock market (and inflation), it is a zero sum game. You aren't creating value by predicting the future. Just like you don't create value when you predict which lottery ticket will win.
1) Reduce spreads.
2) Stabilise prices.
Now, whether it makes any sense to put to work all those bright minds for these purposes, is a question the society should have asked some time ago...
On the other hand, this zero-sum game helps companies raise capital to make real investments with real returns, and that part isn't zero-sum.
Where I think HFT is zero sum is your competing against other HFT people to more accurately and quickly predict the future in the very near term, then buy & sell in a very short period. And since the market changes all the time, these algos must change to stay profitable over time as the competition improves their algos to beat you. Algo trading might work in markets where HFT isn't big yet, but most people won't know which markets that is or how to actually trade there, and if you get good enough to make successful models, you're basically in the industry, it's probably way more than a hobby at that point.