The P-8 isn't the NK-4. The P-8 was a Kuznetsov study for more fuel efficient engines. The P-8 'RVD' is probably better translated as a "propjet", it was hybrid between a turbojet and a turboprop with more emphasis on the jet thrust component than a standard turboprop. Its not a million miles from an unducted fan engine. There was also a turbofan version of this engine. Other engines explored included Mikulin AM-17, Dobrynin VD-5M and VD-7M, and Klimov VK-9F.
The entire 108/100 system was a hybrid bomber, and the 108 was the carrier for the 100. Two mission profiles were envisaged, a strategic one where the host aircraft flies at 900-1000 km/h and a supersonic one at 1500-1800km/h. I would imagine the 'propjet" was optimised for efficiency at the 900-1000km/h profile.
As part of these studies, engine cycles and layout were optimised and later versions had NK-6 engines and a low swept wing.