What is meant by "Who killed the world?"

Now first and foremost, in the movie's setting the phrase obviously relates to the apocalypse, which killed the world as we know it and turned it into the madhouse we see in the movie. So who then actually killed the world? Now seeing that context in which those words are spoken, they're obviously directed at Immortan Joe and his War Boys and the kind of people they represent. It is thus directed at the ruthless dictators and their brutal followers based on power and aggression, incarnated by Immortan and his admirers, who originally killed the world in their power-hungry and brutal ways and who now continue on exactly that path (if not an even more extreme path), especially when seen together with other messages like "Our Babies Won't Be Warlords". The breeding mothers are not just revolting against their opression in Immortan Joe's harem, but even more so for a future where their children will not become like all the other War Boys who once "killed the world".

But furthermore, we should also consider the many feministic themes prevalent in the movie (people better-versed in the respective terminology might excuse me if "feminism" isn't the correct term here, though), be that the whole situation with the breeding mothers, the strong role Furiosa has in freeing them from their opression, the culture of the Vuvalini,... The movie's general tenor is largely seen as feministic by a wide variety of the audience and critics (be it in a positive or negative way), among them also to some degree George Miller himself:

“I’ve gone from being very male dominant to being surrounded by magnificent women. I can’t help but be a feminist,” says George Miller.

...many of the rapturous reactions to his new film, Mad Max; Fury Road, have focused on the dominant role of women in the film, from the fearless Imperator Furiosa played by Charlize Theron to the well-drawn, fascinating quintet of kidnapped wives whom Furiosa spends the film spiriting to safety.

For some other articles reinforcing this notion (but it's really all over the web):

• Who Killed the World? – The Complicated Feminism of Mad Max: Fury Road
• ‘Mad Max’: How Men’s Rights Activists Killed the World
• “Who killed the world?”

Set this in relation to the traits that Immortan Joe and his War Boys represent and I'd say this message can be seen in a much deeper relation to the general patriarchy and violent masculinity that governs the world and is supposedly responsible for its demise. Thus I would say, in the context of the movie, it's the men who killed the world.

The world was ruined by war and the exhaustion of natural resources. The nations that did it, for the most part, were under the control of arrogant, power-hungry men.

Arrogant, power-hungry men killed the world.