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.