Fascist is the correct term. He gives private business the pretense of private ownership, yet he controls the factors of production. Instead of more SUVs, GM will build electric cars at wages determied by the Obama government. Likewise, instead of building trolley cars, Henschel will build Panzer IVs at wages determined by the Reich.
Corporatist is an old word for fascists that dropped out of use around the 1930s or so. It seems to me that once everyone knew that corporatism was bad and would never accept its totalitarianism, the corporatists changed their name to fascism and said look we're not corporatists, we're fascists. If you change the terminology by creating new words, or redefine old words with insidious new meanings, you can really confuse people which causes disunity amongst the opposition Communists/socialists play this same game too by calling themselves "progressives". Albeit, corporatism, is fascism, is tyranny, and we don't want none of that trash.