In non-tournament settings, every dollar you win at poker comes out of the pockets of another player at the table. It's truly a zero-sum game, as adding up the gains and losses of players at the table will result in zero.
In contrast, tournament games (chess, golf, tennis, WSOP, esports, etc) may have significant entry fees, but at a professional level the total winnings are significantly more than the sum of all entry fees. Generally the excess money comes from corporate sponsors or viewership fees. The entry fees can result in some players walking away with less money than they started, but I don't think this is common outside of tournament-play poker.
The most popular professional sports (soccer, football, baseball, etc) have players on salaries. Those players often also get performance bonuses, either for entire-team results (winning the championship) or personal results (number of games played, statistical thresholds, etc). But they're all getting paid _something_ win or lose.
For poker it's actually negative sum at most venues outside of private games due to the fees taken by the organizer (i.e. the rake). But yes, point taken that at least within the closed system of the game poker is zero/negative sum.
My comment was more directed at the OP's assertion that poker is not 'productive' because it is zero-sum. I personally don't see how injecting corporate sponsors into otherwise zero sum games (only one team in sporting events can win, only one chess player can win the tournament) elevates competitive pursuits outside of poker to what can be considered 'productive'. OP's view could be that all of these pursuits are equally unproductive and that would be fair enough.
In order to make money at sports you have to entertain others, i.e. produce entertainment for lots of people. Theoretically, you could win at poker without producing anything, but practically, the most profitable players will be the ones who at least produce entertainment for the people they play with...
In contrast, tournament games (chess, golf, tennis, WSOP, esports, etc) may have significant entry fees, but at a professional level the total winnings are significantly more than the sum of all entry fees. Generally the excess money comes from corporate sponsors or viewership fees. The entry fees can result in some players walking away with less money than they started, but I don't think this is common outside of tournament-play poker.
The most popular professional sports (soccer, football, baseball, etc) have players on salaries. Those players often also get performance bonuses, either for entire-team results (winning the championship) or personal results (number of games played, statistical thresholds, etc). But they're all getting paid _something_ win or lose.