You've pretty much got it. It's called licensing.
The Publisher paid big bucks to Six Flags to use their logos and parks in the game (with the idea being that having a recognizable brand like Six Flags on the cover would sell more games, justifying the expense.) Since Six Flags doesn't own the Superheroes but rather licenses them themselves, the publisher of the game would've had to have paid even more money to D.C., the one who holds the copyrights to the characters, in order to use their names and/or likenesses in the game.
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Touchè, teacher, touchè.