Do I need to follow traditional cover letter style for applying for an academic position?
Here is my opinion based on my rather limited experience:

In the English-speaking world (and probably elsewhere except, perhaps northern Europe) sticking to a traditional letter format is probably a good idea (as if it was being posted). Also it is good to have your contact info on all correspondence materials, especially your email address.

Keep the letter short - one page max.
Start the letter with a Re: (the position applying for) line.
Find out who the search committee chairperson is (phone or email the department secretary) and address your letter to that person with appropriate title (usually Dr. rather than Professor, but in Germany both, if applicable).

Tell them why you want the position, why you want to work at that university (do some homework) and why you are qualified - be enthusiastic.

If it is a research-oriented position (rather than just teaching) emphasise your research interests and how they connect with the faculty there. If just teaching a short paragraph would do.

Let them know that you are available for interview (with blackout dates if necessary) including a phone interview to start with, if desired.