This is something of an absurd claim that does not mesh with how contemporaries saw the Nazis' political orientation nor how analyses of Nazism developed both in the USSR and the US.

For one thing, the NSDAP was a right-wing German political party. It allied itself with right-wing political parties like the DNVP and was seated in the right of the German Reichstag. The NSDAP's striking political successes at the start of the 1930s largely came from the winning over the voters of the various right-wing Weimar political parties; the DNVP, which was among the largest right-wing parties of the 1920s, hemorrhaged voters from the September 1930 election onward. This was something contemporaries observed, see this 1932 cartoon from the SPD-affiliated magazine Der Wahre Jacob. The line of diners with plates of "mandates" are caricatures of various German right-wing political parties ranging from top-hatted businessmen, peasant parties, and neofeudal monarchists.

The NSDAP did manage to peel off some voters from the German left. SPD and KPD party officials at the local level could be aghast at German workers buying into the promises of "real socialism" promised by the NSDAP, even if the latter did paltry little to define its social program. But the NSDAP by and large relied on a bedrock of its electoral support of those voters who were supporters of the various German right-wing parties. The hyperinflation of 1923/24 has largely wedded these voters to the antirepublican right parties, but the German right in the 1920s was a multiparty mess. The strength of the NSDAP was that it could act as an umbrella for what had been as very divided segment of the Weimar body politic. By the same token, most of the NSDAP's ideology such as Völkisch nationalism, unilateral abrogation of the Versailles Treaty, hatred of feminism and the "new woman," and the like were ideas that were most developed within German right-wing discourses and milieus. Nazism refined much of them into something approaching a united platform.

The Soviet response to these developments within Germany was that Nazism and Hitler were manifestations of a terminal crisis of capitalism and the Nazis were the tools of monopoly capital. In this schema, German industrialists were afraid that the Depression would lead to the radicalization of the German working class and they embraced a parvenu rabble-rouser who used the false consciousness of nationalism to stave off a communist revolution. This became the dominant Marxist-Leninist interpretation of Nazism and would continue through the war years (the brief Molotov-Ribbentrop period excepted) and through the Cold War. As the 1979 entry for "Fascism" in the Great Soviet Encyclopedia claimed:

{Fascism is} a political trend that arose in the capitalist countries at the time of the general crisis of capitalism, reflecting the interests of the most reactionary and aggressive sections of the imperalist bourgeoisie. Fascist rule consists of a terrorist dictatorship, headed by the most reactionary forces of monopoly capital and implemented for the purpose of preserving the capitalist system.

The Holocaust did not really enter into Soviet estimations of Nazi barbarity. For one thing, the Soviet state did not brook any rivals to its claim to be the primary victim of Hitler's aggression. The rising tide of postwar antisemitism in the USSR also contributed to a relative disinterest in this aspect of Nazi crimes. Additionally, the Nazis' antisemitism often merged with a larger anticommunism of the NSDAP in Soviet discourses; racism was a tool used by monopoly capital not an end onto itself in this formulation.

The idea that fascism was a tool of monopoly capital meant that Soviet propaganda did not really distinguish much between left and right political figures within the West during the Cold War. Caricatures of Harry Truman in Soviet magazines like Krokodil usually featured the Democratic President as a generalissimo or Mr. Moneybags type (i.e. the most reactionary forces of monopoly capital). This extended to other nations within the Western alliance, as exemplified by this 1973 Pravda cartoon satirizing the FRG military of Willy Brandt using various allusions to Nazi paraphernalia. This hyperbolic line softened after Stalin's death, but Soviet propaganda generally held that both American political parties were potential stalking horses for fascism as both were representative of the interests of the US bourgeoisie.

The American estimation of Nazism in the immediate postwar period went on a very different trajectory than the USSR. The period between the 1950s through the 1960s was dominated by what some historians term the totalitarian model. This model emphasized both the role political terror as well as the dictators' will to power in creating a terror state. Ideology, or the question of left or right, garnered relatively little attention from American scholars in this period. It mattered not what the dictator believed, but how he used ideology to further his own ends. In a highly influential series of writings, Hannah Arendt would argue that Nazism was not so much a special or unique ideology, but a problem of modernity. Her take on Eichmann was that he was not motivated as much by antisemitism as he was fulfilling his duty. This model seeped into popular culture. The episode of The Twilight Zone "He's Alive" argued that racism and bigotry were the foundations of Hitler's particular charisma. The Star Trek episode "Patterns of Force" had a well-meaning Federation scientist adapt Nazi efficiency as a solution to an alien planet's political anarchy. These two genre takes on Nazism denude it of specific political orientation and instead interpret it as a symptom of an unhealthy body politic.

Naturally, the totalitarian model lent itself well to fighting the Cold War. While the totalitarian model as applied to the USSR gave more weight to ideology than when used to analyze Nazism, it still presented communism as a movement geared to a will to power. For instance, the comic series This Godless Communism described the 1917 October Revolution as:

A revolution was organized by a small group of men who urged the people to attack their representative government. The people did this because they thought the communists would help them lead a more comfortable life. The people did not realize that for this promise of an easier life they were giving up their freedom!

There were cracks in the dominance of the totalitarian model within the American academy that emerged in the 1960s. Some popular history works like William Manchester's The Arms of Krupp emphasized the role of German big business in the rise of Hitler. This filtered into various conspiracy theory cranks, but the continued continuity of much of the German business elite between the Third Reich and FRG added credence to these theories.

The idea that Nazism was the hand-maiden of German industrial interests never gained much traction within the American academy. The Abraham affair of the 1980s illustrates this. David Abraham was a scholar of the Third Reich whose book The Collapse of the Weimar Republic: Political Economy and Crisis argued much of the old Marxist line about the Nazism's big business origins. The book garnered some praise, but the American historical profession tore it to ribbons. Henry Ashby Turner in particular savaged Abraham and found much of his research to be shoddy. The Abraham affair revealed some of the squalid nature of academic disputes, but it also demonstrated the limited penetration of the Soviet line on Nazism.

Totalitarianism came under immense strain both as a result of scholarship in Europe on Nazism but also the shift in the American academy away from issues of high politics. This led to a certain rediscovery of ideology within the American academy by the late 1980s and blossomed into the work of the 1990s. This led to an attempt to take Nazism on its own terms and how it as a movement interpreted various political and social problems. This included the Holocaust as a discrete element of Nazi ideology and political policies.

So if a historian like Thomas Childers, Benjamin Carter Hett, or Larry Eugene Jones labels Nazism as a right-wing movement, they are not recapitulating Soviet propaganda. The Soviet line is one that has little traction in academia (although one that has found a home in some corners of the internet) as it took certain precepts as a given. Historians that argue the Nazis are a German right-wing movement are supporting this with actual evidence from the time. It is uncontroversial within the US historical profession to claim that Nazism was a right-wing movement. But what exactly constituted a German right-wing movement in the interwar period is one of the more animating questions within the contemporary academy.