It is a Mickey Mouse account for sure.
The Socialist Party has, throughout its history (and it was around in 1917, don't forget) denied that claim. In fact, we need only refer to Lenin's writings.
One of my fellow SPGB members came across this obscure letter (from 1922) in Lenin's collected works:
The fighting role of the P.C.J. is equally important in the sphere of NEP, and here the P.C.J.’s weakness and apathy is even more outrageous. There is no evidence of any understanding of the fact that we recognise and will continue to recognise only state capitalism, and it is we — we conscious workers, we Communists — who are the state. That is why we should brand as good-for-nothing Communists those who have failed to understand their task of restricting, curbing, checking and catching red-handed and inflicting exemplary chastisement on any kind of capitalism that goes beyond the framework of state capitalism in our meaning of the concept and tasks of the state.
(the full text is here; the italics are Lenin's.)
Lenin saw State Capitalism, under the political control of the Bolsheviks, as a step towards socialism/communism. This we (the SPGB) deny, of course.