I think Pocket had shown me this piece before, but, in any case, I see major errors in Atlas Obscura's piece on Scots.

First, I would call it "Scots English" but Wikipedia in my Google search, sent me to "Scottish English"on that, reserved for Scottish varieties of "received" British English.

Second, there's a number of items to unpack on "language" vs "dialect."

First of all, per friend Massimo Pigliucci, that's definitely a fuzzy demarcation issue. Other examples from the world of languages? Are Mandarin and Cantonese dialects or separate languages? Plattdeutsch and Swiss High German? 

Or, within the matter at hand, British and American English?

Back to the matter at hand.

Wikipedia calls it "an Anglic language variety."

As for "language" vs "dialect," it says:

As there are no universally accepted criteria for distinguishing a language from a dialect, scholars and other interested parties often disagree about the linguistic, historical and social status of Scots, particularly its relationship to English.

To use the British English term, I'll plump again for "dialect." And, while Wiki notes that some scholars do call it a language? "Mandarin" is considered separate language from "Cantonese," BUT ..  In fact, Wiki says "Mandarin Chinese" is one of several varieties of Han Chinese. "True" language of the "Cantonese" type is only in a relatively small portion of southeastern China.

Anyway, the main issue that Atlas Obscura gets wrong is the claim that the Norman Conquest created a break between Old English in Scotland and in England. People who know the history of Scotland-England wars, and Norman barons holding fiefs in both countries by the 1200s, know it ain't so. They also know that there was no "wall" between the two countries.

Wiki's entry on the history of Scots has more. I quote:

After the 12th century early northern Middle English began to spread north and eastwards. It was from this dialect that Early Scots, known to its speakers as "English" (Inglis), began to develop, which is why in the late 12th century Adam of Dryburgh described his locality as "in the land of the English in the Kingdom of the Scots"[4] and why the early 13th century author of de Situ Albanie thought that the Firth of Forth "divides the kingdoms of the Scots and of the English"

There you go.

Did it then diverge? Yes, but AFTER that:

Divergence from Northumbrian Middle English was influenced by the Norse of Scandinavian-influenced Middle English-speaking immigrants from the North and Midlands of England during the 12th and 13th centuries, Dutch and Middle Low German through trade and immigration from the low countries, and Romance via ecclesiastical and legal Latin, Norman and later Parisian French due to the Auld Alliance.

There you go.

As for shifts in pronunciation? Happened within different types of German, too, no invasion involved. 

Otherwise, per that Wiki article and another specifically on Middle Scots, pronunciation and other differences took off from 1400 on.

In other words, what happened was not the Norman Conquest, but Bannockburn and the rise of the House of Stuart, which, to further trump Atlas Obscura, arose from a Norman baron.