The Need For Divine Power.

Chaos is begetting Chaos on its own so he doesn't need to work actively to empower himself. It is like his existence set off a domino of chaotic events. It started as a tiny situation of a low rank demon killing mid rank demons to become a high rank demon threatening the demon lord and will culminate in a war that will take the plane by storm all the while strengthening him in the process. His Accumulation ability is great that way, it is also much stronger than those of other demon nobles. 

Accumulation can be used to raise the state of existence or can be used to attack. He has a divine rank accumulation, he can raise his state of existence from 5 of a high-rank demon to 17 of a demon lord. It is the limit allowed and the increase is also temporary.