If such a Top-Level Domain for Airports makes sense to me, I remember that we already have the .AERO legacy domain name extension which has existed for "centuries" and I don't remember spotting any domain name ending in ".aero" from my entire life.
Just for the note, the .AERO legacy Top-Level Domain was established on December the 19th 2001, and has 20,000 (more or less) domain names created.
I guess that's the question: why would ".airport" domain names catch the attention of all airports worldwide when the ".aero" legacy generic Top-Level Domain kind of "never saw the day"? Is it because ".aero" is a restricted extension, "reserved exclusively for aviation"? Is it because "aero" is too wide and does not offer the precision required to define an airport? Is is because the backend-registry does not contribute more to promoting the TLD of its client? (Roland, I hope you won't read this).
Check the official announcement on www.dotairport.com. The pitch is rather good and delivers the true message why new gTLDs really make sense today.
(I would personally have used the same second level domain but with a ".domains" as the extension to support the project ;-)