I don't believe the Nazis were trying to alter the world in their own image. They were interested in subjugating the world, imposing their hegemony, and using coercive measures, forcing conquered peoples and territories to conform to Nazi policies. Shaping the world in their image is what the Soviet Union did through organizations such as Comintern. The Chinese also adopted the same strategy under Mao and his sucessors, in terms of international interference and the propagation of Chinese Communism.

I suppose you can aruge that the Nazis were more strident and fervent in their desire for what Hitelr called "lebensraum", and hence the expansionist policies.