I think the author forgets that pixels inherently have both width and height, a single pixel, is inherently a 2 dimensional entity, whereas the meter is a purely one dimensional concept. You don't usually talk about whether your meters are the same height as they are tall, or whether they're taller than they're wide.. because they don't have those two dimensions.. You don't talk about how your centimeters are arranged within your meter either.. (you can talk about how your subpixels are, and even if there are 3 or 4 of them).

So, I don't think it's entirely valid to talk about pixels as if they are pure, one dimensional units..

They're _things_ and you can talk about how many things wide or tall something is, and you can talk about how many things something has. Very much the same way you can with bricks (which are mostly never square) (though tiles are, you never talk about how many kilotiles is in your bathroom either, yet you can easily talk about how many tiles wide or tall a wall is).

So, no, pixels is not a unit in the mathematical sense.. it's an item, in the physical sense.

There are also things like scanners, that may have only one row of pixels on the scanner sensor, it does not have an area of zero, and you don't need to specify that there's one pixel on the other axis, because it's an inherent property of pixels that they have both width and height and thus area in and of themselves.