Being Italian I can attest that I spent most of our high-school studying and celebrating such style of writing, and the rest of my life being criticized for it. Dammit ;)
It's interesting to speculate whether Latin supports this style better than other languages like English, or whether it's just a matter of taste.
One difference between these two languages is that classical Latin does not have implicit word order in sentences whereas English is incomprehensible without it. Mentally you have to keep the pieces of a Latin sentence in your head until you reach the end to get the basic meaning. In English you generally know the subject and main verb up front--the rest is details.
The article alludes to it, but I think that English sentences have undergone a fairly major shift since, say, the mid-1800s or so. Maybe even the early 1900s.
I read a lot of older books, and sentences like that aren't uncommon. There's all kinds of strange word orders, clauses piled on clauses piled on clauses, etc. It takes some getting used to, but after a while it quits bothering you. If you made me speculate, I'd guess the Latin education of most English writers had something to do with it.
Nowadays, it's actually quite striking how short and simple most of our sentences are.
I would say that there was a dramatic difference between written text and speech back then, and nowadays that difference is considerably smaller - text has become much more speechlike.
Latin absolutely supports more contorted word orders because the case marking and gender agreement means you can recover hierarchical relations among words in the sentence without relying on word order.
