Learn English – Why are knobs called “pots” by some sound designers

The Oxford English Dictionary doesn't have doublespeak as a separate entry; I can only make an educated guess. The word double-talk already existed in 1938, according to the OED, and was originally American. But apparently it meant simply "deliberate gibberish" then, i.e. not merely ambiguous language, but nonsense talk that listeners were supposed to know meant nothing, uttered to comical or artistic effect.

1938 New York Panorama (Amer. Guide Ser.) vi. 156 Of late a humorously conceived system of language corruption called double talk ... has made itself felt. Ibid. 157 Double talk is created by mixing plausible-sounding gibberish into ordinary conversation, the speaker keeping a straight face or dead pan and enunciating casually or off the cuff.

1941 Time 16 June 61/1 Thirteen recorded versions of this pandemic double-talk ballad are available.

1945 H. I. Phillips Private Purkey's Private Peace xxii. 129 We got the right slant on bullies, greaseballs, double talkers, supermen, and dopes.

1948 Auden Age of Anxiety vi. 125 And all species of space respond in our own Contradictory dialect, the double talk Of ambiguous bodies.

After Orwell's famous novel 1984, published in 1948/1949, double-talk apparently acquired the (additional?) meaning "deceiving language", i.e. language that is deliberately ambiguous, or language that appears to mean one thing but in fact means another.

1950 Amer. Speech XXV. 190 Back in Tsarist times Lenin and his associates inaugurated this double-talk and double-writing—especially the latter—in order to deceive the Tsarist censors and police.

1952 C. Day Lewis tr. Virgil's Aeneid ix. 203 You'll find no Atridae here, no double-talking Ulysses.

This is probably based on Orwell's newspeak and doublethink. His novel was (partly) a critique of the practice and propaganda of the totalitarian regimes of his time, Fascist Germany and Stalinist Russia.

Newspeak is new language invented by politicians as propaganda, in order to influence people's thinking by changing their language (one of the principal mechanisms studied by Postmodernist philosophers and sociologists). The word is invented by politicians in the novel and is an instance of itself. By drastically reducing vocabulary, and making new, simpler words from the remainder, they hoped to control the people more effectively. Many modern euphemisms could be called, and are often called, newspeak, like "differently abled" and "Secretary of Defence".

1949 ‘G. Orwell’ Nineteen Eighty-Four i. 51 Syme was a philologist, a specialist in Newspeak. Indeed, he was one of the enormous team of experts now engaged in compiling the Eleventh Edition of the Newspeak Dictionary. Ibid. ii. 133 Do you know the Newspeak word goodthinkful? Ibid. App. 299 Newspeak was the official language of Oceania and had been devised to meet the ideological needs of Ingsoc, or English Socialism. In the year 1984 there was not as yet anyone who used Newspeak as his sole means of communication, either in speech or writing.

Doublethink is somewhat related to what modern psychology calls cognitive dissonance: first accepting one fact as true, then another, contradictory fact—without critical self-assessment, which would ordinarily result in elimination of one fact or the other. Orwell's politicians try to effect doublethink by means of using and propagating ambiguous language.

1949 ‘G. Orwell’ Nineteen Eighty-Four i. iii. 37 His mind slid away into the labyrinthine world of doublethink. To know and not to know, to be conscious of complete truthfulness while telling carefully constructed lies, to hold simultaneously two opinions which cancelled out, knowing them to be contradictory and believing in both of them, to use logic against logic, to repudiate morality while laying claim to it, to believe that democracy was impossible and that the Party was the guardian of democracy.

Considering the change in meaning of double-talk soon after the publication of Orwell's novel, and the emergence of doublespeak to mean the same a few years later, your sources (reasonably) assume that the word was deliberately coined as a (semi-)portmanteau of Orwell's newspeak and doublethink. The OED has 1957 as its earliest quotation:

1957 ‘M. Buttle’ Sweeniad ii. 55 In the literary weeklies, the languages of criticism and theology have become one and book reviews all sound like sermons written in the most holy ‘*Double-Speak’.

1961 W. Kaufmann in G. E. Myers Self, Relig. & Metaphysics 99 The theologians have a way of redefining terms in rather odd ways, and frequently engage in something best called double-speak: their utterances are designed to communicate contradictory views to different listeners and readers.

The asterisk and quotation marks in the first quote might indicate that the word was then quite new and explained in a footnote.

Nob: There is some dictionary support for the term "nob" as British slang that means either "head" or a "wealthy and important person". EtymOnline gives only one history of the term, and says it means:

"head," c.1700, variant of knob (q.v.).

Wiktionary suggests some other etymologies, both of which highlight that the term refers to someone of high rank:

• From "nobleman" or "member of the nobility" (Doubtful)
• From "white-nob" (Eighteenth century) or "white-head", referring to the powdered wigs used by those affecting upper middle-class status.

Wiktionary also lists possible definitions of "nob" that include (besides a slang term for genitalia):

1. (slang) the head (somewhat archaic): Used in one version of the Nursery Rhyme: Jack and Jill went up the hill to fetch a pail of water; Jack fell down and broke his crown, and Jill came tumbling after. Up Jack got and home did trot, as fast as he could caper; to old Dame Dob to mend his nob, with vinegar and brown paper.

Since there is no one definition, it is possible that the meanings are related. For example, "head" is a literal place that is "higher up", and someone who is important is figuratively "higher up". Despite the multiple definitions, one cribbage site gave some history, mentioning that "nob" is the "term for noble or superior person".

Depending on the definition used, the term is either from around the late 16th to early 17th century. Since cribbage was invented around this time, "nob" could refer to either one of these meanings.

Whichever meaning it refers to, either the figurative or literal definition of "nob" meaning head or important, the rules of cribbage build upon the notion of importance:

The nob Jack (or "right Jack" as it's also known), is essential for scoring a perfect 29 hand, and also affects discard strategy - you should try to avoid throwing a Jack to your opponent's crib if possible.

So the "nob Jack" is a strategically important card, and its name possibly derives from this.

Nib: @Kit mentioned that some people refer to "his nibs" or "nib" instead of "nob". This is another somewhat accepted term that has similar origins. There is, however, some debate about which is correct:

Throughout Cribbage history, the term “nibs” and “nobs” (or “his nibs” and “his nobs”) have been interchangeable. However, with the rise of Cribbage Inc., and its lesser president Robert A. “Nibsmonger” Laird, many serious cribbers among us have begun to research which one is the correct one. Although most have reasoned that “nobs” is the correct term, many (most notably the “Nibsmonger” himself!), refuse to yield “nibs”. Many a cribber has argued in vain to come up with a solution, and the debate rages on to this day, and probably will until the end of time.

Whichever term is "historically accurate", nib has a similar meaning as the slang nob. Wiktionary says that one definition is:

(slang, UK) An important or self-important person.

This is slightly different from the aforementioned definition of "nob", but it still seems to refer to someone who believes he is (or is) important. The term "his nibs" has entered into the vocabulary of some, which lead one person to ask for its origins:

This is a mock title used to refer to a self-important man, especially one in authority.... Also, nib itself was once used as a slang term for a gentleman, as was another old slang word still to be heard, nob, and these could very probably be connected. Several early examples of the latter are spelled nab and his nabs is a variant recorded form of his nibs. It seems the vowel was highly fluid, not surprising considering the different dialects and periods it has come through.

The last point brought up in this article may point to the reason there is a "nib/nob" debate--vowels have come to be pronounced differently over time.