He never said such a thing if you carefully read what you have posted, let me quote an excerpt.
On page 9 at the bottom he quotes the hadith narrated from Abu Hurayra in the footnotes "whoever speaks Arabic is an Arab"
Ibn Taymiyyah also quotes the following hadith which he considers authentic in his footnote of what you presented (other scholars dispute it's authenticity)
Oh my people! God is one and the same. Our father is the same. No one amongst you inherits Arabic from his father or mother. Arabic is a habit of the tongue, so whoever speaks Arabic is an Arab" (al-Ittijah al-Qawmi fi al-Shi'r al-'Arabi al-Hadith: 216)
From the research I have done on this topic, Lisan al Arab was widely spoken outside of the Arabian peninsula, it's what English is today, Latin was back in the day etc. Even the Habashi's in Yemen spoke it, we also know "Salman Al Farasi" that came from Persia spoke it.
Keep in mind Hebrew/Aramaic before this were also widely spoken and these are semitic sister languages, anyone that would have studied scriptures those days would have known classical Arabic as well, the Jews in Medina did, we know some roman slaves that later became the best of companions like Suhayb ar-Rumi spoke the language, there is no description of any translators whatsoever or them being taught the language.
Ibn Taymiyyah postulates that the Persian's likely in those days spoke Lisan Al Arab too from what you posted. This makes perfect sense because the greatest contribution to Arabic grammatical analysis of the Quran came from Persian scholars, and these were very early in history.
There is no doubt the Muslim who knows or learns classical Arabic (not the junk spoken today which is not the type of Arabic being talked about) is superior then the Muslim who doesn't speak it, because such a person has a better connection to Allah's book.
Those that speak the Junk Arabic (shameful to call it Arabic) don't even understand the Quran at all when it's recited, I met many of them during Umrah 7 years ago and who didn't even speak any form (classical or junk) had 100x better understanding then they did.