Four-day tickets don't and door tickets don't, but online you can book Kombi day tickets that include rail travel within the VRR. For the benefit of people who aren't mid_gen, that covers the Rhein-Ruhr region including Dusseldorf, Dortmund, Bochum, Duisberg, Oberhausen and Mulheim.
We also found out this year that travelling from Essen to Dusseldorf Flughafen by taxi can be as cheap as €53 depending where your hotel is. If there's three of you in the taxi this is only €5pp more expensive than the train even if you're within walking distance of Essen Hbf, and you don't have to carry that heavy suitcase full of games.
Your hotel should handle the booking for you if you ask; just be sure to make certain the company knows you have big bags so they can send a larger car.