Corporatism actually already had a definition and this isn't it. See: Mussolini.
Discussion
It's not so much rule by corporations, but rather, treating the society as a single body, or "corpus." There is definitely some overlap, but it's a bit more integrated and less ad-hoc than this idea of corporatism. Crony Capitalism though is a fine name for this other thing. Could also probably go with corporatocracy.
Yes the definitions are different but they functionally work the same way in essence. Treating society as a corpus is the same thing as statism. Crony capitalism is statist capitalism. Same thing.