It is a zero-sum game as long as you define it as follows: a trader's score for each transaction is (price paid - closing price). If Alice sells GOOG at $100 to Bob, and GOOG closes at $99 that day, then we say that Alice won $1 and Bob lost $1. That's all.
Maybe 1 year later Bob will sell GOOG to Alice at $200, and the stock will close at $201. Again Alice won $1 and Bob lost $1.
Of course Bob made a lot of money in the process, so the zero-sum game definition might sound arbitrary. However, as far as trading is concerned, the definition as zero-sum game is useful. If Bob were a better trader (more skilled or luckier) perhaps he could have saved $2.
See The Winners and Losers of the Zero-Sum Game by Larry Harris.