Regional offerings are run under request by the state and often as part of regional organisations run by involved cities, who have a say on the fare. Only long-distance travel (starting at 100km) is done by fully DB on their own rules.
In this case the stations are in the area of the Verkehrsverbund Berlin-Brandenburg (VBB; Public Transport association of Berlin and Brandenburg) Inside this association there is a quite complex pricing system, as in the one end it covers densely populated areas like the city of Berlin as well as hardly populated areas further away from Berlin.
For full details there is a 79 page brochure with all sorts of tickets: http://images.vbb.de/assets/downloads/file/1564472.pdf (German only, apaprently) and a summary in English on http://www.vbb.de/en/article/tickets-and-fares/ticket-fares/ticket-fares/5649.html
The gist is "In rural areas the price is the result of driven kilometres. For more information please ask the hotline."
For your ride the Fare calculator on http://fahrinfo.vbb.de/bin/query.exe/en?application=TARIFFONLY& calculates "Between 25 and 35 km" as price category between Köngis Wusterhausen and Tropical Islands and "Between 35 and 45 km" for Wildau to Tropical Islands, which seems plausible since routes from Wildau seem to go via Königs Wusterhausen and looking at the map distance from Königs to Tropical is about 30-35km.