right wing" despite the fact that most economical ideas of nazis were socialist to begin with.
On paper perhaps and if you selectively quote them. Goebbels for example admired Lenin because of his demagogic talent and deemed his way to power as an example (Hitler on the other way admired Mussolini more).
Something to generally keep in mind that back then it was way more acceptable for even right-wing conservatives that the state should play a large part in the economy. The Nazis however were mostly content with leaving the industry in the hands of their current owner, only telling them what they needed for the future (especially for the army).
They enacted a few token social laws to appease the lower- and middle class, but they did so for the same reason as Bismarck once had done, to get their agreement for the new order. The communists and social democrats were in 1933 and later the biggest possible opposition to them, and the Nazis feared nothing more than something like the Spartacus uprising. So naturally they'll try to neutralize this source of discontent. Again, this is basic history. Communist dictatorships have already enough blood on their hands to show how bad of an odea they are, there is no need to artificially add Hitler to the list.
But...how should they know? Did you ever take a look at the party program?
Well, the German Wikipedia makes a better job of explaining that the party program from 1925 became quickly obsolete afterwards. It had the same role as the Weimar constitution after 1933. Pro forma it still counted, but nobody cared and it was deliberately ignored when necessary.