Answer
The entire planet has the same rotational speed, but at the equator, the tangential speed of surface material is the highest. The material is pulled by gravity toward the center, but the high speed means that a stronger centripetal force (to keep the material moving in a circle) is required than if the material were located elsewhere. Gravity does win, but bulging occurs to increase the distance from the rotation axis (and relieve the need for too much centripetal force).
An argument can also be made by appealing to the concept of fictitious force in a non-inertial rotating reference frame, pages 147-148.
