Donald Trump's run-on sentences

In every Trump speech, almost every sentence is a run-on sentence. Here is a quote from one of his speeches last year

Look, having nuclear—my uncle was a great professor and scientist and engineer, Dr. John Trump at MIT; good genes, very good genes, OK, very smart, the Wharton School of Finance, very good, very smart—you know, if you’re a conservative Republican, if I were a liberal, if, like, OK, if I ran as a liberal Democrat, they would say I'm one of the smartest people anywhere in the world—it’s true!—but when you're a conservative Republican they try—oh, do they do a number—that’s why I always start off: Went to Wharton, was a good student, went there, went there, did this, built a fortune—you know I have to give my like credentials all the time, because we’re a little disadvantaged—but you look at the nuclear deal, the thing that really bothers me—it would have been so easy, and it’s not as important as these lives are (nuclear is powerful; my uncle explained that to me many, many years ago, the power and that was 35 years ago; he would explain the power of what's going to happen and he was right—who would have thought?), but when you look at what's going on with the four prisoners—now it used to be three, now it’s four—but when it was three and even now, I would have said it's all in the messenger; fellas, and it is fellas because, you know, they don't, they haven’t figured that the women are smarter right now than the men, so, you know, it’s gonna take them about another 150 years—but the Persians are great negotiators, the Iranians are great negotiators, so, and they, they just killed, they just killed us.
[Source: Slate magazine]

I understand a run-on sentence is usually just something like:

It will be dark soon we can't be home before nightfall.

Is Trump's typical speech habit considered multiple run-on sentences? Or what would the term be. And being a speech, is this an error in English language in general, a grammatical error on his part, something else, or no errors at all?

EDIT: Since I have received negative comments over the quotation, I would like to clarify: I don't care about the quotation, I googled an example of a Trump speech to use for reference and found this. Since I apparently found a bad quote, or maybe something he never actually said, here is a different quote for reference. Note that I felt it would be inappropriate to replace the main quotation since this question has already been answered and I feel altering it would be unfair:

And in 19 — and I will tell you this, and I said it very strongly, years ago, I said — and I love the military, and I want to have the strongest military that we’ve ever had, and we need it more now than ever.
[Source: The Wall Street Journal]

Similar to the (bad example) speech above, this quote has Trump starting off with one thought, going to the next, interrupting himself to mention his love for the military, and then closing without finishing either prior thoughts. I didn't know what this was called, and was unsure if there was a term for this speaking style and whether or not it was in violation of any English rules.

It’s something else. I might not agree with Trump, but he is not incoherent or committing grammatical errors. When a person speaks extemporaneously or “off the cuff”, unless they are well trained in the art of public speaking, this example is a typical result. What you are seeing is mostly the three common forms of self-interruption:

• parenthesis, interrupting to insert a clarifying remark
• self-repair, interrupting to go back and edit an error
• filler, interrupting to signal that the speaker is thinking: words like uh, like, and you know

A transcription that preserves every instance of self-repair and filler, such as this one, is probably intended to ridicule rather than to preserve the utterance. The usual practice in journalism is to eliminate self-repair and filler in quotations unless there is something significant about a misstatement.

Also, in a transcription, the audible and somatic (gestural) content of the utterance is lost. Without that information, the utterance can seem much more random to the reader than it would have to the audience.

Trump’s thoughts are poorly organized, but he does a remarkably good job of remembering where he was before each self-interruption. In computer science terms, he commits no stack overflow errors.

The transcript below makes the parenthetical structure of the example clearer with indentation, and de-emphasizes the self-repair and filler. What emerges is a coherent utterance, close to what the audience would have comprehended.

Look, having nuclear

—my uncle was a great professor and scientist and engineer, Dr. John Trump at MIT; good genes, very good genes, OK, very smart, the Wharton School of Finance, very good, very smart

—you know, _{if you’re a conservative Republican, if I were a liberal, if, like, OK,} if I ran as a liberal Democrat, they would say I’m one of the smartest people anywhere in the world

—it’s true!

—but when you're a conservative Republican _{they try—}oh, do they do a number—that’s why I always start off: Went to Wharton, was a good student, went there, went there, did this, built a fortune—_{you know} I have to give my _like credentials all the time, because we’re a little disadvantaged

—but you look at the nuclear deal, the thing that really bothers me—it would have been so easy, and it’s not as important as these lives are

(nuclear is powerful; my uncle explained that to me many, many years ago, _{the power}

and that was 35 years ago;

he would explain the power of what’s going to happen and he was right

—who would have thought?),

but when you look at what’s going on with the four prisoners

—now it used to be three, now it’s four—but when it was three and even now, I would have said it’s all in the messenger; fellas,

and it is fellas because, _{you know, they don’t,} they haven’t figured that the women are smarter right now than the men, _{so, you know,} it’s gonna take them about another 150 years

—but _{the Persians are great negotiators,} the Iranians are great negotiators, _so, and _{they, they just killed,} they just killed us.

Verbal diarrhea ought to be the technical term. I don't like using the Urban Dictionary as a reference, but in this case, I think it is right.

A condition suffered by an individual who has the inablility to shut the f--k up, i.e the words keep flowing

While the term run-on sentence suggests a grammatical phenomenon, it is a punctuation error. For example, Merriam–Webster defines run-on sentence as:

a sentence containing two or more clauses not connected by the correct conjunction or punctuation

So, every run-on sentence can be made into something else by proper punctuation. For instance, your example run-on sentence can be made non-run-on as follows:

It will be dark soon; we can't be home before nightfall.

It will be dark soon. We can't be home before nightfall.

As punctuation is a feature of written language, run-on sentences cannot occur in spoken language by definition. Nobody can speak a run-on sentence, not even Donald Trump.