Umm, ‘universally-known’ is rather an overstatement, wouldn’t you say? I doubt most lay people are familiar with even 10% of the jargon that floats around in academic linguistics. Even something quite common like transitive/intransitive is probably not a familiar term for say (just guessing off the top of my head) 50% of the general population.
But even before that objection: First of all, prior to the widespread study of linguistics in English (which has come to be the world’s lingua franca (somewhat ironically)), I’m pretty sure the Japanese would have used their own words to describe their own language (just a wild guess). And while I don’t know enough about the origins of Japanese to say what words were used when, the Japanese do currently use the words 自動詞 (jidoushi) and 他動詞 (tadoushi) to describe words for which the subject is ‘self-moving’ or ‘other-moving’.
In the video Cure Dolly gives the example of 従う (したがう) meaning ‘to obey’, which is listed in Jisho (したがう - Jisho.org) as an ‘intransitive’ verb, even though the English equivalent is transitive. See, for example, this primary definition which illustrates that, taken at face value, it actually is a transitive word in Japanese:
- to obey (an order, law, etc.); to abide by (a rule, custom, etc.); to follow; to observe; to conform to; to yield to
But it is also a 自動詞, and hence that is why it is ‘translated’ as an ‘intransitive’ verb in Jisho, even when functionally speaking, it is not – because ‘self-moving’ and ‘other-moving’ are not typical distinctions made in most Western languages, so some time in the past Western linguists mapped 自動詞 to ‘intransitive’ and 他動詞 to ‘transitive’, because those were similar concepts which they already were familiar with, even though it’s not a perfect mapping. However, when considering the ‘hyperliteral’ meaning as ‘self-move’ versus ‘other-move’, it makes perfect sense: One obeys another person (transitive), but the one doing the obeying is oneself (自動詞).
Just because the linguistics terminology might (currently) be considered ‘universal’ (and actually I doubt that, unless linguistics is a dead subject with no active scholarly research and debate), that doesn’t mean that every language in existence must conform to those prescribed concepts/definitions. If Japanese functions in such a way that their distinction between 自動詞 and 他動詞 is meaningful within Japanese itself, then who are we to argue? It is what it is.
Personally – and this is solely just my own opinion on the matter, not meant to be persuasive to anyone else but me; just a little ‘aside’ – I like how Japanese is a little bit (sometimes quite a lot) different than Western languages. It’s interesting. It’s fun. I’d like to learn more about how/what it is rather than trying to fit everything into some pre-existing conceptual framework developed largely because of the historical accident that the modern study of linguistics flourished most in Western countries, where Western languages all have a lot of similarities with each other that don’t necessarily map directly onto other languages of the world.
Before I move on, I want to mention that: Second of all, if transitivity is such a universally understood topic, then why such confusion over it when it comes to how Western sources try to teach Japanese? Could it possibly be the case that there are subtle differences between the way Japanese works as a language, and how Western languages typically work? 
Hyperliteral? Hmm, let’s see:
- 自動 - automatic
- 自動車 - automobile
- 自動販売機 - automatic vending machine
- 自動化 - automation
Meanwhile:
- automatic - having the capability of starting, operating, moving, etc., independently
In other words, ‘self-moving’, as opposed to ‘not taking an object in a sentence’. I think a more accurate descriptor would be ‘literal’ rather than ‘hyperliteral’.
I also doubt if ‘na-adjective’ is a universally-known linguistics term. 
But to answer your question, I have indeed added 形容動詞 to my SRS queue (on a different site) when I first discovered that it’s quite different than a Western-style adjective, and indeed I also learned it on WK at around level 21 a while back, before I reset from level 28 down to level 7, and I did indeed use the WK vocab (along with 形容詞 and 動詞) as a way of learning that it can combine aspects of both adjectives and verbs. Indeed, it can be said to be neither an adjective nor a verb, but actually a noun(!), as described in this snippet from Wikipedia (Adjectival noun (Japanese) - Wikipedia):
In fact, by some analyses, nouns and na-nominals are fundamentally grammatically the same, where 〜の vs. 〜な when used attributively is simply a conventional stylistic complementary distribution, with 〜の／〜な being allomorphs. This view is reinforced by the fact that some words, such as 特別 tokubetsu “special”, can take either a 〜の or a 〜な, depending on the phrase.[1] Ultimately, 〜な is an abbreviation of 〜にある, used to use a noun attributively (compare modern 〜である, which is a more recent form), while 〜の is the genitive case;[1] see etymology, below.
It’s when it’s combined with a copula (e.g. da or desu) or with na itself (which as shown above is originally an abbreviation of a verb) that it takes on its ‘descriptive verb’ aspects. Quite an interesting and useful thing to know!
Huh! Who would have thought that looking into the ‘hyperliteral’ meanings of Japanese words (in particular their etymologies/origins), especially in relation to Japanese itself, could shed such light on otherwise arbitrary-seeming conventions, and actually make learning Japanese more logical and even fun! Who ever would have thought?!?! 
I do? Really? Are you sure of that? Heck, I often make up words-that-don’t-exist-yet-or-at-least-I’m-not-aware-of-them all the time when I’m trying to explain something to someone else. As long as myself and the other person ‘get’ what exactly it is that I’m talking about, what’s the problem?
In fact, I would suggest that approaching language more flexibly, as a way to convey intended meaning/feeling rather than as some strict and/or judgmental system (“You’re not conveying your meaning in The Correct™ way, even though the other person understands you just fine!”) is actually a very useful approach. Don’t knock it till ya try it, as they say.