In Ticket to Ride: Märklin, do Passenger cards allow you to complete Destination tickets?
It is important to note that passenger cards are not used to claim routes. Although they are drawn like train cards, they are not played when claiming a route. They are played only when using the Move Passengers action to collect Merchandise tokens from cities. Each passenger card played allows you to move your passenger through one route belonging to another player.

Excerpts from the rulebook:


  [When Moving a Passenger] The player may move any one of his Passengers that is already on the board. The Passenger must move from the city he currently occupies along any or all of the player's continuous routes, picking up one Merchandise Token from each city
  he moves. The player can only use the same route once per turn, i.e., a Passenger may
  not backtrack over the same route. The player does not pick up a Merchandise Token in the city in which the Passenger starts. At the end of the turn the Passenger that moves is removed from the game.


And the role of the passenger cards:


  When moving a Passenger, the player can play any number of Passenger Cards and use one route belonging to an opponent for each Passenger Card played.


(p. 3-4 of the rulebook)

Passenger cards do not give you any ability to use opponents' routes for any other purpose, including completing tickets at the end of the game.