This paper describes in detail why the USSR is state capitalist and provides a lot of interesting analysis. I’m just gonna copy-paste a few paragraphs:
A private form of any class structure is one where the individuals occupying class positions – and especially the positions of appropriators/distributors of the surplus – are not officials, functionaries, or employees of any state apparatus. In contrast, a state form is one where individuals occupy class positions in their capacity as state officials or their appointees. The histories of both capitalist and feudal class structures exhibit mixtures of private and state forms.
In most conventionally designated ‘capitalist countries,’ private capitalist enterprises prevailed whose producers and receivers of the surplus held no posi- tion within any state apparatus. Yet state capitalist enterprises usually also existed in those countries: often, state officials or their appointees received the surpluses generated by wage laborers within commodity producing enterprises. In the USA, for example, state capitalist class structures have existed, among other places, in the Post Office, the Tennessee Valley Authority, municipally owned utilities, state universities, public radio and television, and Amtrak.
What the Soviet revolution did achieve was a transition from the prevalence of private capitalism to that of state capitalism instead. This transition was associated with particular redistributions of wealth and power and particular cultural shifts (e.g. hostility to organized religion). Thus, the events of 1917 and after in the USSR challenged and frightened many within societies where private capitalist class structures still prevailed. They reacted by criticizing the USSR as the actualization of ‘communism’, that evil ‘other’ of capitalism that they had long demonized as a godless, dictatorial, and unworkable dystopia. Since the critics had no conception of the distinction between private and state forms of capitalism, they reasoned instead in terms of an epochal contest between capitalism (simply equated definitionally to private enterprise) and communism.
After Stalin’s consolidation of power in the late 1920s, Soviet society was officially described as an actually existing socialism whose goal was an eventual transition to communism (the latter defined as a kind of egalitarianism which took ‘from each according to his ability’ and distributed output ‘to each according to his need’). The USSR after 1928 thus defined itself as socialism and socialism as the opposite of capitalism. Celebrators and critics alike ignored or excluded the concept of state versus private capitalisms in relation to what existed in the USSR. Thus, nearly everyone viewed the global contest of the 20th century as capitalism versus socialism.