I've looked as well. The article you refer to, and others by Bennetts and MCN, refer to the law for guidance in Ingurlund.
I have a feeling that the law is different here. Didn't they make a lot of things law at the beginning of December in order to give the police more powers to deal with the National Park visits? I fear that recreational use of bikes might well be in there somewhere, but I can't find any details!