The design is fictional.
The boosters appear to be adapted from this schematic of the Soyuz, with some roman numeral and Cyrillic letter call-outs pulled from other parts of the drawing, but with the boosters redrawn to have three nozzles each, and a new core stage drawn with 15 nozzles. No Russian engine design that I'm aware of uses a three-chamber design analogous to the 4-chamber engines used on Soyuz, and there are too many similarities between the Soyuz schematic and this design for it to be coincidence.
I went through Asif Siddiqi's "The Soviet Space Race With Apollo", which describes various Soviet heavy launcher designs both real and notional, and none of them bore any resemblance to this one.
This interview with an animator who worked on the credits suggests that much of the imagery was adapted and redrawn from real sources, and I believe this rocket design is such a case.