From the first paragraph the Wikipedia page about the Nazi Party has been corrupted by leftists.
Socialism is not “right wing”. Socialism and communism are scattered next to each other in the wasteland of left-wing ideas, but because Hitler lost his battle he was disowned by the left and thrust onto the right.
Hitler’s National-Socialists and Stalin’s communists were both leftists, and leftists always end up in a struggle with each other for ultimate power. It’s what they do. Every. Single. Time.