I would consider day-trading (by which I mean people sitting in front of their screens, buying and selling assets when they find it appropriate based on (to me very mysterious) indicators such as chart patterns, usually holding their positions only for one day) to be a zero sum game, in the following sense: Consider a market $A$ in which everyone holds their assets and there is (almost, see the footnote* below) no trading, and consider a market $B$ which is full of day-traders and everyone is constantly swapping assets.
In market $B$, nothing more gets produced/manufactured/provided to the people than in market $A$, and furthermore, at any given time, the assets present in market $B$ are identical to the assets present in market $A$. So the additional trading in market $B$, beyond what is needed for the market to be "efficient" (in some vague sense), adds no value to the market, which is why I would consider it a zero-sum game.
In this post it is claimed that
Day traders also engage in buying and selling of securities. According to research conducted by JM Chung, Hyuk Choe, and Bong-Chan Kho, day traders tend to couple with longer term investors, buying and selling from these investors, rather than each other. The authors analyzed data made available by the Korea Stock Exchange. According to the analysis, this activity reduces the bid-ask spread, which indicates that the practice increases liquidity in the stock market. Therefore, when there is a shortage of normal buyers and sellers in the market, day trading activity allows the investor to buy and sell securities as needed, without suffering from excessive spreads. While I don’t have an extensive amount of data on the topic, I would argue that there is a net flow of value from the investment traders to the day traders, which acts as a “payment” for that liquidity.
Is there any evidence to support the last sentence? And does it even make sense? (For example, if there really are pricing inefficiencies caused by there "being to many long-term investors wanting to sell" at a given time, wouldn't financial institutions be able to make use of this much more quickly and precisely than any day-trader? And isn't the behavior of long-term investors as hard to predict for any individual as a random walk, so that I don't see how to make money from that consistently (cf. this)?)
* There still has to be some trading, since I would like my hypothetical market to be efficient in the sense that it can react to new information and so forth quickly, which is clearly impossible if there is absolutely no trading at all.
