Because writers don't speak epub yet? I realize your question was hypothetical but there are a zillion things that generate PDF out there and only a few that generate EPUB or other mobile friendly format.
I find it funny that the author suggests people read it on their Kindle when PDFs render so unreadable there.
Honestly, I got as far as hovering the link, saw it was a .pdf by the status bar, and was instantly alienated.
What decade was this fictional start-up created in? 1870?
Because there are iPads and other tablets today that can do them.
Is there something particularly strange or unique about this story's formatting that it couldn't have been rendered in HTML?
No. But PDFs are really seeing a resurgence thanks to tablets, especially the iPad. It's the one kind of formatting that's pushbutton and done. Anyone who uses Word can create one. [typo edit]
Because it offers superior typography than epub/mobi.
Because you can use it on your desktop/laptop/tablet AND phone (even on your Kindle I hear).