In all other cases except the Triwizard cup, portkeys only go one way at one specific time. Touching them again does not activate them to return to their place of origin. Also, when Harry grabs the cup a second time, it does not return him to the middle of the maze. It takes him to the entrance of the maze, in front of everyone.
Therefore, when Crouch Jr. (as Moody) bewitched the cup, he planned to have it take anyone who touched it first to the graveyard, then to the front of the maze.The cup was probably supposed to be a portkey to take the winner to the front of the maze anyway, so they wouldn’t have to try to fight their way out again.