This is just to let you know that on my way to the airport tonight I met two young ticket inspectors on the Skytrain, who rigorously controlled everybody's tickets and assured my that the Skytrain was gebührenpflichtig. I told them that I had thought the Skytrain was part of the airport infrastructure, like a shuttle between terminals. I had a VRR Preisstufe B ticket, which is valid on the Skytrain, and I always have this when I go to the airport.
Tip: a bit OT, but in the VRR area of Nordrhein-Westfalen it's worth getting a 10er Ticket which is available for smartphone only. A Preisstufe B 10er Ticket costs EUR44, which (at EUR4.40 a ride) represents quite a saving on the normal single ticket price of EUR5.80. Going to Düsseldorf city would be Preisstufe A, which is a lot cheaper, and you can get a 10 ride ticket for that too. These are valid for one way journeys only, and are valid on the Skytrain in one direction connecting onto/from other train and S-Bahn services.