The question Performance of a pumpless liquid rocket engine is thoughtful and provocative and pretty much all answers include a mention of the extremely high pressure necessary to push propellants into a high pressure combustion chamber and the use of turbo pumps for this purpose.
But this is based on steady-state combustion in the chamber, and the rotating detonation rocket engine is a horse of a different color.
Question: Would rotating detonation rocket engines always require high pressure fuel pumps?