This is called time dilation but had nothing to do with it being a gravity experiment.
The fact that the plane accelerated, traveled and moved at a different rate of speed to the stationary clock is what caused the dilation, not the high/low relative positions.
The theory affecting gravity's effect on time is not the experiment you reference here. THAT theory says the effect is the opposite of what you are offering here, that gravity slows time down. But one needs to be in the proximity of a very large gravity well for the effect to be noticeable i.e. a black hole. The Earth is not a large enough gravity well to cause an effect we are capable of measuring at this time. A "frame dragging" experiment is under way however which will measure the effect of the Earth's rotation on gravity and time.
To the outside observer, one who approaches a black hole does not age, he actually slows down to the point that the external observer never sees him fall into the hole, just get closer and closer to it, according to this theory. The one who is doing the falling notices nothing at all as far as time is concerned. Remember, it's all relative on what frame of reference (FOR) you use to measure.
The clock in the plane ran slower due to accelerated dilation. If it were gravity slowing one of the clocks, it would be the one on the ground that ran slower. This is/was not the case, quite the opposite.
