Here's another explainer: http://www.nytimes.com/2015/10/08/insider/when-death-comes-a...

The obit for Steve Jobs was initiated 4 years before his death.

All publications of a certain size pre-write obits. This isn't unique to the Times.

A similar way that reports of boxing matches come out very quickly after the end of the match - because they didn't wait for the end to start writing.