Not necessarily. We all know of the theory of Mutually Assured Destruction.

As an analogy, think about what happens if a deadly infectious bacteria or virus "wins" by infecting every human on earth. If there is no cure and no human has an adaptation or mutation to stop it, by winning it has sowed the seeds of its own destruction because there are no more hosts to infect.

It is easy to imagine several scenarios where an all out war for dwindling resources can lead to extinction.