No that's an oversimplification. I can ride a bike because I want to ride a bike. But terrorism by definition describes a type of tactic used to reach a stated goal. It is not simply killing people. That's called murder. And murder can be an end to itself. There have certainly been murderers who had a compulsion to just kill.

Terrorism is killing a lot of innocent civilians in order to incite terror in a population to bend to your demands. They have an agenda and feel they are justified.