Say a day trader buys a stock for $9/share and then sells it to me at $10/share a week later. I then put the stock into my investment portfolio and hold on to it for forty years and sell it at $100/share. You could make a simplistic argument that the day trader "lost" the game because he missed out on the appreciation to $100/share but you are neglecting the different investing timespans. The day trader doesn't have a job if he is holding on to stocks for 40 years. He was happy to buy and sell quickly for a small profit. I'm happy because I held on to an appreciating asset. Bankers are happy because they made a few dollars in commissions. No one losses here.
But you two are not the whole market. Someone sold a stock to a day trader and someone bought it from you. There are no other money in a stock market except those people bring (minus commission) so how everybody can win?
That's exactly what happening - the only source of money are participants, and part of the money goes to brokers.