I believe you are conflating the concepts of "currency", "wealth", and "value."
Here is an example I used with my kids once. Let's say you went the Pittsburgh Pirates game in 1978[1] and you caught the first home run hit by then rookie Barry Bonds. If you sold it in 1978 you would have been lucky to get $50 for it, if you sold it in 2007 when he retired with 762 home runs you could have gotten significantly more for it, perhaps several tens of thousands of dollars, and if you sold it in 2011 after he was tainted by steroids you would get less.
But in all that time, the ball was just the ball. It's value went up, its value went down. As it went up and down the value of other home run baseballs also changed in value, but in ways completely unrelated to the value of Barry Bond's first home run ball. If you owned every single home run ball from the major league the value of any one ball was only related to that ball's history and not to the other balls.
Quantitative analysis of markets is the art of figuring out how to recognize the value of something is changing before others do, and capture that value by acting on that knowledge. Whether it is offering to buy Barry Bond's first home run ball because your model suggests he could become an all time home run hitter, or selling it in 2009 because your model suggests Barry is likely to be tainted by the steroid scandal in baseball.
You didn't steal any money, you didn't change the amount of "value" in the market, and the amount of "value" in the market it not controlled by a fixed number, its controlled by other events completely outside of your control. You bought something before others knew it would be valuable, you sold it before others knew it would be less valuable. Definitely not a zero sum game.
[1] http://m.mlb.com/cutfour/2015/06/04/128375782/watch-barry-bo...
Of course, once you add in the realities of uncertainty and much longer time periods, you can make more subtle arguments about risk exposure, hedging, etc. But in the simplest case, trading on privileged information is absolutely zero-sum, at least in the sense that there's a clear winner and loser (and in the stock market, it's illegal!)
> Definitely not a zero sum game.
Grandparent comment is right and you seem to misunderstand the idea of zero-sum. A transaction is zero-sum if it doesn't change the amount of value. The stock market is mostly zero-sum. The only non-zero-sum transactions are when firms sell their own stock to get spending money. The only added value of the stock market is choosing which of these transactions should happen. Since front-running doesn't affect these transactions, I think it's safe to say that front-running is zero-sum.
To extend that analogy the trading company has a tap on the Reuters newsfeed and they sell the ball as soon as the steriod story reaches them, milliseconds before it reaches the newsrooms.
