Some airline tickets include the SkyTrain fare, but I don't know which airlines. In addition to VRR/VRS tickets, DB City+, NRW, Schöne Reise, Schöne Fahrt, and Schöner Tag tickets are also valid for the SkyTrain, as are observation deck tickets and parking garage tickets.
http://www.duesseldorf-international..._en/b_skytrain

I've been checked twice on the SkyTrain, but it really seemed more like a survey than "enforcement" (e.g.,both times the checker was carrying a clipboard on which s/he wrote down numbers). No one was fined, and the checker was satisfied with airline tickets from seemingly any airline. Someone was told that they needed to get a ticket in the future, but there was no big to-do.