It is actually the same case as airport. “Backpfeifengesicht” consists of just two nouns like “airport” does. Not that the classification really matters here as far as I can tell.

You cannot say the words separately and assume it still makes sense in either case. It is losing its meaning, the words on its own have a different meaning than the compound word. That’s what I am saying. Without this specific word you would have to say it in a similar fashion as in English.