Zero-sum game is a bit too strong. A more general and realistic assumption is that the no trade point is on the pareto surface. One trader's gain must be at the expense of another.
One important and closely related question to poster's, is, from a game theoretic perspective, why trades occur in finanial market, or its weaker version, why trades in finantial market of a narrow sense occur in such a high volumn, even taken diversity of risk preferences and asymmetric information into account.
As pointed out in Nameless's answer, in basic Lucas tree model, assuming homogeneous traders, there's no room for trade. The market price of asset is totally determined by the conditions that guarentee a representative trader has no incentive to buy or sell a piece of an asset.
Even worse, Milgrom and Stokey(1982) shows that ex ante pareto optimality of no trade point is incompatible with common knowledge at some state that no trader is worse off and at least one of them is strictly better off after a non-zero net trade. Noticeably, the result of no trade is obtained by only assuming traders are all risk-averse.
In conclusion, there's some element of truth to see trade in some market, say, stock market, as a zero-sum game, despite of the existence of a more realistic alternative assumption. Diversity of risk preferences is far from the whole story of why trades occur. As an attempt to explain it, noise traders has been hypothesized by some behavioral economists.