Who cares what Marx defined, he couldn't even properly define his own novel ideology.
I'm pretty sure he did, he wrote multiple books on the subject. The Nazis did not want international revolution, they sought the expansion of their own nation and of the aryan race. For why rejection of internationalism is important in whether the nazis were socialist, I'll refer you to Engels.
— 19 —
"Will it be possible for this revolution to take place in one country alone?"
"No. By creating the world market, big industry has already brought all the peoples of the Earth, and especially the civilizedpeoples, into such close relation with one another that none is independentof what happens to the others.
Further, it has co-ordinated the social development of the civilized countries to such an extent that, in all of them, bourgeoisie and proletariathave become the decisive classes, and the struggle between them the greatstruggle of the day. It follows that the communist revolution will notmerely be a national phenomenon but must take place simultaneously in allcivilized countries – that is to say, at least in England, America, France,and Germany.
It will develop in each of these countries more or less rapidly,according as one country or the other has a more developed industry, greater wealth, a more significant mass of productive forces. Hence, it will goslowest and will meet most obstacles in Germany, most rapidly and withthe fewest difficulties in England. It will have a powerful impact on theother countries of the world, and will radically alter the course of developmentwhich they have followed up to now, while greatly stepping up its pace.
It is a universal revolution and will, accordingly, have a universal range."
I don't intend to throw buzzwords at you, you just don't want to be reasonable with me. Marx literally states what I mean by "advanced commodity economy" in the first sentence of Capital.