Doesn't desolation mean a state of complete emptiness or destruction?
So why doesn't Smaug perish by the end of the 2nd Hobbit film if the film's title was made to describe his end? He only dies at the start of the 3rd film: Battle of Five Armies. Does Jackson say why?
It means "the desolation caused by Smaug".
In the book, this is the description given to the barren area around the Mountain, specifically to the south and west. (The map displays north to the left.)
In two days going they rowed right up the Long Lake and passed out into the River Running, and now they could all see the Lonely Mountain towering grim and tall before them. The stream was strong and their going slow. At the end of the third day, some miles up the river, they drew in to the left or western bank and disembarked. ... The next day they set out again. ... The land about them grew bleak and barren, though once, as Thorin told them, it had been green and fair. There was little grass, and before long there was neither bush nor tree, and only broken and blackened stumps to speak of ones long vanished. They were come to the Desolation of the Dragon, and they were come at the waning of the year.
The Hobbit, Chapter 11, "On the Doorstep"
The Desolation of Smaug does not mean the Destruction of Smaug.
Definition of desolation
- the action of desolating
the pitiful desolation and slaughter of World War I — D. F. Fleming
- grief, sadness
... he put his trembling hands to his head, and gave a wild ringing scream, the cry of desolation. — George Eliot
- loneliness
- devastation, ruin
a scene of utter desolation
- barren wasteland
looked out across the desolation
desolation — Merriam Webster
So while I see how you thought The Desolation of Smaug meant Smaug being laid to waste, a more likely explanation is using the fourth meaning as given above: the barren wasteland around Smaug's lair in the mountain Erebor.
Of course, one of the other meanings could apply as well: the sadness or loneliness of Smaug or the grief or devastation caused by Smaug.
Now let's turn to the book.
The land about them grew bleak and barren, though once, as Thorin told them, it had been green and fair. There was little grass, and before long there was neither bush nor tree, and only broken and blackened stumps to speak of ones long vanished. They were come to the Desolation of the Dragon, and they were come at the waning of the year.
The Hobbit, "On the Doorstep"
This quote, along with the map, clearly shows that it's indeed the fourth meaning that's used here, the barren wasteland around Erebor, which is what the party had just reached in the quote.
Of course, as is the beauty of any language in which words can have several, related meanings, all these meanings are invoked when used in the film's title like this.
But it is clear that it does not mean Smaug being laid to waste.
