Luck tends to even out in all games that involve luck if you play long enough. Why is it different in bridge than in poker? Luck will even out in both.
It's not that different, if you can play enough rounds. Bridge and poker both give you that chance over a day. Magic the gathering, not so much.
However, the luck element (by the human way of thinking about luck, not my definition) is much smaller for duplicate bridge than for poker. You can get legitimately screwed by finding the right contract and going down due to unusual opposing hands, but so will most of the rest of the field bidding your cards. _Only_ unskilled players will get a good result on that kind of hand, and they will give you back that advantage later. I guess you could say that the correlation between skill and score is negative on a few hands.
A pro player on a cold streak will usually lose a few bucks in a cash game against new players, but a professional bridge player will beat the new players, guaranteed, even with the new players making "happy accidents."
I also did attempt to define the luck/skill axis in a way that is non-intuitive, but I believe correct when talking about games in a technical sense: luck games have information hidden from all players, while skill games do not. In that sense, bridge is not a luck game. It is an unfair game because you can get screwed by how the cards are placed around the table, but the unfairness tends to even out as you play more hands.