How to address the german “Prof. Dr.-Ing. habil. X” in writing?

No, just "Dear Professor X" is correct and completely in line with the German conventions. The "Dr.-Ing. habil." part refers to certain qualifications (PhD in Engineering and a Habilitation -- a German qualification to teach at a University), but is only ever used on name cards and CVs etc.

If you yourself are not a German academic, I am certain it would be quite fine to refer to him as "Dear Professor X" rather than specify the full academic title. I've heard people refer to German academics using this abbreviation (although, frankly, not in German).

I also suspect that this would be ok even if you are a German academic and are writing him in German - but that's pure speculation on my part, based on how it's unlikely you're supposed to use such long titles. Edit: Comment seems to verify this.