"Professional" in the context of visual design is about the aesthetics of business (as opposed to the aesthetics of, say, amateurs). I didn't mean professional in the sense of "money-earning," as you would use the term applied to participants in a certain field.
Exec's launch website is unprofessional because it is unpolished, visually unresolved, and appears to have taken little time to create. I don't want to break down into a detailed argument over specifics, but the biggest problems have to do with spacing, type size, the crappy icons, and the hyper-generic elements like the buttons, background tiles and color palette. Also, the logo (which isn't very distinctive in and of itself) isn't even used throughout.
The redesign is very carefully proportioned and arranged. It uses somewhat less generic colors and buttons and so forth, and some simple visual ideas are repeated throughout to create a sense of continuity and harmony. Each section flows well from on area to the next.
Again, I think you might be projecting a little bit. Who's "hung up" on "unreasonable standards" of professionalism? The post is about a person redesigning Exec's landing page. The redesign is more professional, looks more polished and refined and careful, than the original. I don't think that's a huge deal, and I don't think that makes Exec a huge failure or something. I'm not insisting that they raise their design to any standard.
EDIT: FYI, I'm not really much of a web designer myself. Kyro can probably define the problems with the existing site in much more detail than I could.