I don't know if the article writer is north American, or possibly not familiar with traditional/native English, else they would know they are completely wrong it not being English.
The author wrote: "I can't use "else" as a conjunction in normal speech, only in computer programs."
No doubt people use 'else' as a conjunction now, due to the influence of programming.
To show the author is completely wrong requires finding pre-1959 uses of 'else' in a conjunction.
Google ngrams shows 'else' being used fairly consistently up until about 1880 after which it gradually declines. In the 2000s it rapidly picks up, probably because of the programming influence.
Looking at the actual texts, there are a few German ones listed. Plenty with "someone else", "nothing else". Quite a lot with "or else", for example: "Yea , but what am I ? a scholar, or a schoolmaster, or else some youth".
The Wiktionary entry at https://en.wiktionary.org/wiki/else lists three use forms;
Adjective: When all else fails, read the instructions
Adverb: How else can it be done?
Conjunction: Then the Wronskian of f and g must be nonzero,
else they could not be linearly independent.
The "someone else" and "nothing else" examples you listed are the adjective form.
The "or" in "or else" is the conjunction, not the "else".
You should be looking for something like " "Yea , but what am I ? a scholar, or a schoolmaster, else some youth".
Another thing to check would be if earlier uses were only in binary exclusive cases, like "One if by land, else two if by sea", or also with 3 or more terms, like "One if by land, two if by sea, else three if by air."
I don't know how to carry out this sort of search.
I did find this example, however:
> "My brother is poor, and I want to look as much like him as I can, else he may feel distant from me."
From Mill on the Floss, published by George Eliot in 1860.
With "else he may" as a search time, I found other examples in archive.org, like https://archive.org/details/sim_christian-intelligencer_1835... from 1835 .