Jake in the comments asks:
Actually it's a good question, not stupid at all. It does help management and here's how.
Say that ticket holder you purchase the ticket from is a season ticket holder who purchased their ticket directly from the Bengals. That person has to buy a full season ticket package each year at a pretty high cost or they will lose their COA. If that person believes they can sell off the tickets for the games they can't go to (or make money selling them above face) then they are more likely to keep buying season tickets each year since they don't have to keep taking a loss on tickets they don't use (or even make money).
Same for a scalper. Scalpers are more likely to buy tickets if they think they can sell them easily. Anyone selling or buying tickets from anyone who is not the Bengals is dealing in what is called a secondary market. The primary market would of course be buying tickets directly from the Bengals.
Anyway, secondary markets reduce the risk that someone will take a total loss on an investment since they can resell to others in a secondary market. In this way secondary markets can drive demand in the primary market. It's not a direct transfer of money to the Bengals but it indirectly helps them in a very meaningful way by keeping demand for tickets high. You just have to go beyond the first level of analysis. (Incidentally, for nerds or gambling addicts, here's a cool article that discusses a market for ticket options and futures - derivatives - on the secondary markets for tickets)
Anyway, don't help the secondary market, Jake, tempting as it may be. Boycott.