What does the aperture pixel number actually refer to?

Aperture has an effect on depth of field when that feature is enabled. The AE camera simulates a full frame 35MM still camera with a 24mm X 36mm image plane. The film size is measured horizontally. Any time you fiddle with any of the settings in the camera you end up with a "custom" lens.

The most meaningful part of the camera controls is the angle of view. This is because perspective is controlled by camera position and framing is controlled by focal length. The depth of field depends a lot more on distance from the camera than it does on the angle of view, even though both are important when setting up a shot.

For example, if you have a 50mm lens at f28 and the lens is focused at 10 feet everything from 9.08 feet to 11.13 feet will be sharp when the image is examined at a normal distance. Changing the film size, putting the 50mm lens on a 35mm motion picture camera (horizontal with 24mm), won't change the depth of field, it just changes the framing. Changing the focal length to 35mm and f2.8 changes the depth of field so that everything from 8.19 feet to 12.83 feet is acceptably sharp. Not perfect, but acceptably sharp at a normal viewing distance. 

So to summarize a 50mm lens at f28 gives you an acceptable in-focus range of 2.05 feet with the lens is focused at 10 feet and a 35mm lens at f2.8 gives you an acceptable in-focus range of 4.64 feet.

If you have set up a shot of something like a car with a 50mm lens and you want to change the perspective but keep the car the same size in the frame you have to move the camera and change lenses. If you put on a 35mm lens and move in so the car still occupies the same percentage of the frame you'll have to move the camera closer. To keep the same basic framing you would need to move the camera from 10 feet to 7 feet. The wider lens gives you more depth of field so you would have an acceptable in-focus range of 2.08 feet. To get the same depth of field and the same framing with a 35mm lens that you get with a 50mm lens you would have to move the camera from 10 feet to 7 feet. The difference in the in-focus range would be 2.08 feet, which is not very significant but if you wanted to precisely match the focus depth you would need to slightly open up the lens.

I hope that makes sense. Only about half of the professional photographers that I know really understand focal length, framing, perspective and depth of field. AE's camera works on those same rules. The aperture increases the range of acceptable focus, the closer the camera is to the subject the shorter the distance between DOF near limit and DOF far limit, and perspective is controlled by position and framing by focal length.

I hope this helps you figure out how to better use AE's camera and how to better use your real camera.