The left-right political spectrum was established during the French Revolution of 1789, so the question is legitimate.
A quick search of JSTOR reveals a number of pre-WW2 articles that refer to the National Socialist Party of Germany as right-wing.
The last election to the Reichstag brought the unexpected and rather extraordinary rise of the National Socialist German Labor party from twelve to 107 seats. It is the party of the extreme right.
See Nature and Aims of the National Socialist German Labor Party (page 377).
The new elections on July 31, from the experience of the past and the symptoms of the present, should mean further gains of the Nazis, and to such an extent as to establish beyond doubt the predominance of their party, with the right wing coalition over the middle and left wing groups.
See Herr Hitler Comes to Bat (page 107).
The Nazis polled something more than one-third of the total vote and returned 230 members to the Reichstag - their largest number up to this time - but they did not succeed in securing a majority even when combined with the other Right parties.
See Germany Today (page 39).
On the Right, as I said before, there were large groups in opposition [in 1928-29]: there were the moderate Conservatives who had taken part in government and remained in the coalition. They were beginning, however, to lose their followers, who turned further to the Right [i.e. to the Nazis]. There was a second group - the German Nationalist Party, then coming under the leadership of Hugenberg, the party which stands for as much restoration of the pre-War Constitution as can be achieved, the followers of the old regime who have remained true to it and still hope for a return to the old social and political order. This party, once very large, split up when a new, very much more vigorous and more active movement of opposition, the National Socialist Party, grew up under the leadership of Hitler. The followers of Hitler have been recruited very largely from those parties which once formed the Moderate Conservative Wing of the "nationalist opposition."
See The Crisis of the Democratic Régime in Germany (page 761).
So, that is at least four contemporary articles that described the Nazis as part of the right wing, and indeed the far right of the wing.
Pinsdorf seems to be especially authoritative because she appears to have sympathised to some extent with the Nazis, relating to their views towards the Jews.
The fourth article, by Arnold Wolfers, goes on to explain the "socialism" of the Nazis, which is worth a read (pages 761-763) if you can download the article.
It was uniformly viewed as a right wing party, and it viewed itself that way, more importantly.
There's two ways of going about determining the left- or right-wing nature of the NSDAP. The first is consider what it means to be left- or right-wing generally and then apply it to Nazi ideology. The terms "left-wing" and "right-wing" come from the French Revolution, during which the revolutionary parties seeking to abolish the monarchy and establish a republic were seated in the left wing of the national legislature, while monarchists and defenders of the ancien regime were seated on the right. While the right-wing was thus associated with the ideas of hierarchy, tradition, and resistance to change, the left was associated with egalitarianism, progressive social thought, and rapid social change. (Of course, these associations are imprecise -- not everyone on the left opposed egalitarianism, and the left, once empowered, often established its own hierarchies). Given its dedication to a strict racial hierarchy and the radical traditionalism that it expressed in terms of issues like gay rights and women in the workplace, it's easy to see why the NSDAP was on the right. It thus sought (and found) natural allies among the more mainstream right wing parties in Germany and ultimately formed its government with one of them (the DNVP).
More specifically, why this question sometimes emerges (other than simple bad faith assertions by the likes of Jonah Goldberg, Dinesh D'Souza, and Steven Crowder) is the revolutionary nature of the NSDAP, the dedication to some of its members to a robust series of social programs and wealth redistribution, and the use of the word "socialist" in its name -- NSDAP stands for Nationalsozialistische Deutschearbeiter Partei, i.e., National Socialist German Workers' Party.
First, the use of "socialist" in the name was, more than anything else, an attempt to attract working class urban voters to support the party. That said, as noted, there was a not insignificant wing of the party, led by the brothers Gregor and Otto Strasser, that emphasized the socialist elements of the party platform to a greater extent than Hitler and his wing did -- both before and after seizing power. That said, two factors should be considered: first, the "socialism" of the NSDAP was predicated on the exclusion of non-Germans and specifically Jews and thus was inherently exclusionary to begin with, whereas socialism generally was considered to be inclusionary, if not outright internationalist. Second, this wing of the party was the one that was eventually eradicated in the Night of the Long Knives, and in practice while in power, the NSDAP actually privatized more of the means of production than they placed in government or public hands. Finally, bear in mind that even the so-called "left wing" of a far right party is still on the right.
The last thing to consider is whether the revolutionary nature of the party would characterize it as right wing. Here, the answer is again no, for while the tactic of revolution would certainly be more often associated with the political left, if the goals of the revolution are inherently right wing in nature, then so is the party waging the revolution. A good point of comparison here is the Islamic Revolution in Iran in 1979. Yes, it was a revolution, so we might be tempted to consider the revolution "left wing," but in power, the revolutionaries established their key goals, which were returning to a more traditional Islamic way of life, reversing the progress of women's rights, and eliminating parties on the political left.
With the attempts of people like Crowder and Ben Shapiro to continue spreading the notion that the Nazis were left wing, there's a lot of information out there addressing this point. Stanley Payne's A History of Fascism: 1914-45 is a good introduction to the right-wing taxonomization of the NSDAP compared to less revolutionary right wing forces. Much of the material refuting the "Nazis are leftists" idea consists of videos, and the effort from the Youtuber known as "Three Arrows" is among the best: https://www.youtube.com/watch?v=hUFvG4RpwJI