Experience will count for a lot, possibly more than a degree. Saying a degree is desirable/required is so that you get a reasonably educated person who can carry out tasks like writing reports, work to deadlines etc applying.
I used to be an LA (local authority, not Los Angeles…that would’ve been awesome) Cycling Officer and really enjoyed it, wish I was still doing it rather than ‘general’ highways design I do now.
If you want the job, don’t be a pessimist and apply for it and see what happens, you’ll almost definately get an interview at the very least IMHO. :-)