The World - Fairly Earth-like. Most of the action here is taking place in a grassland and light forest on a small continent. Several human civilizations exist. They are mostly small city states with shaky alliances, no large spanning empires. Technology is similar to Dark Ages Europe, about 500AD. This question will be dealing with two of the civilizations:
The Tribe - A former loose confederation of nomadic tribes, now unified and lead by a Chief Warlord. Though perceived as savages by some of the Kingdom, the Tribe actually has a sophisticated culture. They have many of the same types of artisans, religious leaders, nobles, etc. that the Kingdom has, but the social classes are not in a strict caste system as theirs is. Most are herders or hunters, but some settle in the few cities. Somewhat lower standard of living than the Kingdom, but much more personal freedom. They respect the Kingdom's technological and economic achievements, but see their crowded cities as unnatural and morally corrupting. Their army is fairly well developed. Most regional warlords are expected to commit a certain amount of soldiers to a war and to guard against border raids. Additionally, there is a centralized trained army for larger engagements. Due to numerous small wars with a third nation (neutral in this war), they are much better prepared than the Kingdom.
The Kingdom - A small empire, one large central city with a few smaller walled settlements. They consider themselves the pinnacle of civilization. Some want to "share the greatness" with the rest of the known world, but the majority of the Kingdom is pacifist/isolationist including the monarch. They are definitely advanced in the arts, sciences, and economy, but are severely lacking in military. As in, they can build cathedral-style buildings and monuments with ornate stonework and metalworking, but they haven't applied these to military fortifications and weaponry. Their capitol is reasonably fortified, though the walls are aging and poorly maintained. They have lived in a relatively peaceful time for several generations, during which the military has been downsized. Their military now consists of a small amount of well trained professional soldiers, a few mercenary groups usually hired as caravan guards, and militia/town guards with minimal training.
The War - One thing leads to another, perhaps some Kingdom noble insults a tribesman or some hunter kills a farmer's herd. The point is somehow or other something sparks the mutual hatred the two hold for each other. I'm leaving this ambiguous as it may lead directly to an answer. The Tribe starts border raids against the Kingdom. The tension and intensity of the conflict escalate, and eventually turns to all out war. The Tribe quickly pockets the small Kingdom army in the capitol and lays siege to it. Leaving the majority of their force at the capitol, the Tribe also sends raiding groups to the other smaller towns to eliminate other pockets of resistance. Their nomadic way of life makes their supply lines and outposts more natural. The Kingdom previously had active internal trade routes which would have led to better supplies, however the swift raiding and siege cut these largely undefended routes. Within less than a year from the initial conflict, the capitol falls and the Kingdom is defeated.
The Desolation - So here's where things get interesting. Rather than just pillaging and/or making the Kingdom a tributary state, the Warlord orders the Kingdom utterly destroyed. Citizens killed, buildings burned, monuments torn down, the whole total annihilation thing. Some citizens are able to escape, but the Empire as a whole is desolated.
Given the above information, why would the Tribe completely destroy their enemy? It seems logical to me that after defeating an economically superior foe, you force them to pay tribute. I am basing the Tribe loosely around the Hephthalite Empire. After a series of wars and raiding, they forced the larger, more influenctial Sassanid Empire to pay regular tribute for many years. The Hepthalites even supported their own puppet king of sorts with Kavadh I. In this historical example, the complete destruction of the Sassanids would have proved disastrous for the Hephthalites, as their combined forces were able to hold off the Romans from Sassanid territory. I've set up my story with the destruction of the Kingdom as sort of a background story, but it seemed less and less realistic as I progressed. While I appreciate creativity, I am looking for reasoning and historical examples rather than "what if this happened?"