Dami and Needle, you aren’t reading the right info.
The OP refers to the flightaware page that does in fact show number of based aircraft. Someone else posted the airnav link that shows operations.
At my old airport we would fill out a form every year that we listed the numbers of the aircraft on the field. I don’t know whether this was for the state, the FAA, or the AOPA directory, but similar forms must exist for these numbers to be compiled and published.
To answer the OP’s question, the info probably comes from the FAA in one way or another, and is probably the product of some sort of form that the airport ops/ FBOs fill out.