[MalbertKerman]

Combustion cycles that run the turbopump exhaust into the main combustion chamber are called "staged combustion." The Soviets had staged combustion engines putting payloads in orbit in 1960, and the US flew its first in 1981.

SpaceX's advance was going from oxygen rich (where all of the oxidizer and a fraction of the fuel run through the preburner and turbine, as used in the Soviet/Russian engines) or fuel rich (vice versa, used in the Space Shuttle) to full flow (which has both oxygen- and fuel-rich preburners and all of the propellants flow through one turbine or the other).