Short answer is no, mostly they are not counted. Even if they have this data it is very unlikely that they publish it.
Assuming that you are not a transfer/transit passenger; meaning you have arrived to airport by ground transportation for your departure and you have left the airport via ground transportation when you have arrived; you will be counted as 42 times in the statistics (21 departure + 21 arrival). This is standard counting method.
If you arrive to the airport by a plane, you stay inside the plane and you leave the airport with the same plane; then you are a transit passenger which is counted 1 time.
(You are not a departure or arrival passenger, you are a transit passenger)
If you arrive to the airport by a plane, you leave the plane and you leave the airport with the another plane; then you are a transfer passenger which is counted 1 time.
(You are not a departure or arrival passenger, you are a transfer passenger in this case)
So passengers of an airport are basically; departure + arrival + transit + transfer
(Note: Exact definitions of transit and transfer might change from airport to airport)
Most of the time, especially in smaller airports, airport management does not record passengers on a unique person basis. They simply don't have the unique identifier for each passenger, such as a passport ID number. So they cannot know if a person is travelling first time or fifth time.
However, there are exceptions of course:
There are (very expensive) software that allows airport management to record, filter, manage each passenger data with extreme detail. Its work logic is that it records a special text message that airplane sends to airport before arrival.
For "international" departing/arriving/transfer passengers, this unique traveler information can be obtained from the system of the passport police since they record ID numbers of passports.
Airlines might have this data separately; however this is not a feasible approach since airlines mostly do not share this info.