From the output I can understand there was no errors, yet there aren't any answers section to the query. Just to be sure the right question was even asked: "Dig +norecurse @s.nic.dk MX www.dtu.dk" parsing this to: "without recursion, query dtu mail exchange servers through the nameserver s.nic.dk"
Is the query not supposed to return nameservers of dtu MX?
No, it isn't supposed to, because you are asking the authoritative name server of the TLD (s.nic.dk) for the answer. It does not have this answer, but gives you the details of the name servers that do: that is why you receive the authority section (and additional section).
However, even if you do query the authoritative name servers (for example: @dns1.dtu.dk) there is no MX record for the domain name www.dtu.dk, but rather for dtu.dk. Which means your query should be: dig @dns1.dtu.dk MX dtu.dk.
For note, the addition of +norecurse shouldn't make a difference when you're querying an authoritative name server directly.
