You’re right that the gate was probably still being used, but the airport doesn’t control gate assignments, the airline does. The airlines lease the gates from the airport and control which flight goes to which gate.
That part isn't totally accurate. The gates at nearly every major hub airport are shared to some degree. At DFW American runs A&C but B/D/E are shared space. Most hub airports have a split to some degree with certain positions owned and others shared.