This is a great question. We should answer this question in a few different ways.
On a physical level, Napoleon does not die on the farm. He is alive and well at the end of the story. However, he does cause others to die. For example, he was the architect of a massacre.
On a more literary level, we can say that the old Napoleon did die. The Napoleon that earnestly wanted a revolution died. Once the revolution took place, he betrayed the principles of it. At first it was small - the taking of apples and milk, but by the end of the story, he introduced a rule of terror.
If we focus on the final scene of he book, we can also say that Napoleon died. He is no longer a pig. He turns into a man. From this perspective, Napoleon, the pig, is gone forevermore. He is now a man.