Not to be a smart ass, but a "population reduction war" is, by virtue of the words placed in that order, a war fought to reduce population. It is, I posit, a logical conjecture about a hypothetical future war. It's not too difficult to foresee something like this. Combine the prime problem of exponentially growing population pressure with the exacerbating factors of dwindling resources, kin selection, religious friction, ideological conflicts between neighbors, and energy-dense technology proliferation and you have the perfect ingredients for a return to our species roots as genocidal monsters.
A war fought for territory, or for honor, religion, or for ideology would be completely different than a "population reduction war." A "population reduction war" would be a war fought specifically to reduce the population on the Earth. Whether this ultimate goal is know or hidden from the participants is irrelevant. In a population reduction war killing the enemy's armed forces is not done to force compliance, depose the government leaders, or to gain territory. Killing the enemy would not be a means to an end in a war like this. Killing the enemy is the end. And, as such, the means would be different than in other wars. Combatants would not be the main targets, they would be tactical obstacles between you and the strategic goals of large populations of civilians.