Basically, the virtual aperture for a telephoto lens design is right at (or very slightly behind) the front element. The real
aperture is smaller, but that doesn't matter in terms of element size - it's the virtual aperture that has to be filled with light (for other lens designs, e.g. retrofocus lenses like UWAs, the front elements are apparently much larger than they 'need' to be - it's a different design). What Chuck is saying is the 70-200/2.8 has a real, physical aperture that approximates 70/2.8 (e.g. ~25mm), and that the elements in front of that physical aperture 'magnify' it to form the virtual aperture, which gets larger as you zoom to longer focal lengths.
You get a sense of that from the block diagramL
When looking at one of these, though, it's not just the position of the iris diaphragm or the sizes of the elements relative to the approximated size of the iris diaphragm - you also need to consider the elements themselves, whether they're converging or diverging lenses. Roger Cicala wrote a series on the basic lens designs a while back, on his lensrentals blog (and IIRC, CR reposted here with permission) - worth a read.