I think the point here is if your plane flys either towards an oncoming rotational axis or away from one.
(Basically moving the goalposts of the landing strip to either be moving away from you or towards you.)
If it's moved towards you while your fly towards it, your going to reach their sooner than if it hadn't of moved.
If your flying towards it and it's moving further away then obviously it's going to take longer than if it hadn't of moved or if it moved towards you.
The appearance here is that you gain or lose time because your travelling for either a shorter or longer duration based on rotational spin, since the earth doesn't sit still while you fly around it.
Note here that you might point out that you can play catch with a ball in a car, as long as there is no high speed speed increase or decrease you can pretty much catch it in the same spot.
However when your talking about an aircraft that doesn't mearly go up for the brief period of time before gravity kicks in, this relationship of the ball being hurled in relative momentum has no effect. Namely while an aircraft is airborne it no longer has anything to do with the Earths Gravity in the sense of why your still standing on it's surface and not flying off.