I had a similar case with McKinsey 5 years ago, so I think I can share some details given how long ago it was (2nd round, partner interview).
A lot depends on where the partner leads you. There are many ways to do the estimation, but if the partner leads you in a certain direction, you need to follow it. In my case, the partner ignored my attempts to do the estimation from the demand side and asked to identify and estimate from the bottleneck perspective. The bottleneck for airport is, as was correctly mentioned above, runways - you probably experienced many times the need to sit in the airplane and wait when a runway becomes available.
So, the rough equation would be: # hours an airport operates * # runways * (# minutes in an hour / # minutes it takes a plane to take off/on) * # passengers per plane * load factor. That's the generic approach, now you can adjust it to account for non-passengers, support staff, by, for example, finding out a number of passengers and then assuming a ratio of passengers to non-passengers.