“Polonius” didn’t die because “Polonius” is not a real man. “Hamlet” never stabbed him, save within the story written by Shakespeare, because “Hamlet” is not real person. To claim “Polonius died” is to suspend disbelief (to pretend the story is real and not written
by Shakespeare,) and so within that context we must say that Polonius died because Hamlet stabbed him.

We might ask “Why did Hamlet stab Polonius?” and I think it is here that we would exit the story to reference its author. If one would make the claim made above for this case we can see such logic leads to a series of “why?” questions ending with a final “why?” that must reference the author.

I see two places where the author might be referenced as a cause in a story: the first is in the will of the characters, and if not there then in the first story event to which all other events form a chain reaction.

Yet, in the end, the question is negligible. The words of Shakespeare broken down to an ordered series of letters broken down to a dark chemical absorbed by paper mean what you interpret them to mean. The real question, as with all art(and even technology,) is: Does it help you understand reality?