An MSX-ENGINE chip is a specially developed integrated circuit for home computers that are built according to the MSX specifications.
This is done to reduce required circuit board space, power consumption, and (most importantly) production costs for complete systems.
The last generation of MSX, the Turbo-R used the NEC S-1990 "TurboR bus controller" together with a R800 CPU.
Note that this IC is also used in many MSX2 computers, but does not include any MSX2-specific functions.
In such machines, these are implemented using additional IC's The S1990 is not in itself an MSX-engine but acts like "bus controller", it is the combining element that combines the Z80 inside the T9769C (the actual MSX engine) and a R800 CPU, and the memory and slot logic and other hardware inside the T9769C.