As an NLP person it's very hard for me to endorse this explanation, because the Vaswani et al transformer (as it is described here) simply does not work until you add the most important ingredient of all: the positional encoding.

Most of the semantics of a sentence are indicated by the precise order the tokens appear. This is easiest to see in a language like English, since it is visible in two very prominent ways.

First, the morphology is fairly derivational, meaning you can keep adding suffixes to things and English speakers will generally get what you mean. For example, add some more suffixes to that word: derivational-ish-ly. You've probably never heard this specific variant, but you still probably have some idea of what it means anyway. The transformer can only capture these semantics if it has some representation of the fact that the suffixes inflect the meaning of the word's root (presumably something like `deriv`). English encodes this entirely by the position of the suffixes relative to the root. Without the positional information, there is no way to recover it, and sentences would lose much of their meaning, since English depends heavily on this construction.

Second, English has relatively few cases, and thus relies very heavily on the order of words to indicate what is the subject and what is the object. English specifically is Subject-Verb-Object, and the instinct of native English speakers to use SVO ordering is so strong, you will find them inserting nouns and pronouns into sentences that do not actually have subjects at all. "It's raining outside" is the most famous example. This sentence has no subject at all, and yet native English speakers feel a strong need to place "it's" at the beginning.

If the transformer did not have positional encodings it would be completely hopeless to recover what is the subject and what is the object from English sentences. There simply is no other way to reliably tell, other than inspecting the word positions.

It's worth noting we also do have the counterfactual. Generative language models that explicitly exclude positional information, like Latent Dirichlet Allocation, are only able to (essentially) cluster word co-occurrences. That is not as useless as it sounds—if I say "fire house burning ambulence" you kind of get the point even without a subject or an object—but it certainly does not generate the lucid, provoking sentences that modern LLMs do.