From the intro of the page you link: "The orthographic depth of an alphabetic orthography indicates the degree to which a written language deviates from simple one-to-one letter–phoneme correspondence."
So, sure, if you want to discuss about how English orthography is deep, go for it. I won't even really disagree. Quite the contrary.
The opening claim was that it wasn't phonetic, though. That is a different thing.
It is funny seeing Japanese as the first example in your quote, as it has both a phonetic syllabary (two, actually) and a non-phonetic logography. That is, you literally have to learn to read a non-phonetic orthography in order to read Japanese!