An engine is a device that converts potential energy into mechanical work. Our rocket motors are engines because they convert the chemical energy stored in the propellant into the motion of the rocket.

Rocket motors based on solid propellants are generally called "motors" rather than "engines" though it is not incorrect to call them "rocket engines" as Estes does.  The term "engine," however, is usually reserved for liquid-propellant rocket engines with a large number of moving parts.