The more common argument for stock trading being zero sum is that if I experience a gain after buying a stock from you, you experience an equal loss (by selling the stock when it would have gone up).

Dividends do not alter that argument in any way. The trade is described as zero-sum because the total amount of value it produces is zero -- in the trade scenario, I gain X, and in the no-trade scenario, you gain X. X minus X is zero. My gain is your loss.