Why is electric force represented as a vector?
Forces act in a direction.
The definition of a vector quantity is one that has both magnitude and direction. A force, regardless of its type, acts on an object with direction.
For example, if you are pushing a box with a large mass across the kitchen floor, the pushing is a force; the force is being applied to the box in the same direction as the movement of the box.
Electric force is no different. Electromotive force acts upon the electrons, causing them to move around the circuit in the direction that the force is applied.