I think he means that
A pixel is not a little square: http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
Fair enough, his description seems misleading. To me a pixel is a discrete RGB value, which is made up of physical components, for example:
Where / in what way is it implied that pixels don't have size? What is "redefined"? I think the article explained the concepts very well.
From the article:
"Asking someone what the size of a pixel is is a good way to confuse him or her because it’s a trick question. A pixel has no size, no physical value or meaning outside of its mathematical representation. It is a part of a relationship between the physical screen size, expressed in inches, the screen resolution, expressed in pixel per inches and the pixel screen size, expressed in pixels. Laying it all out, it looks like this:"
"As you might have noticed in my explanations, “Resolution” stands for PPI, in this case “109” but not “2560x1440”, like you might commonly see everywhere on the web."
Edit: Actually the first paragraph of "Resolution, pixel and physical size" kind of really causes confusion, since he is trying to redefine standard definitions, and then tries to provide reasoning for the redefinition. This is mainly a note of caution.