Oh, huh, I guess I forgot that detail. That makes that even more interesting then. In a metaphorical sense he still killed her, but it's not quite the same dramatic sacrifice as the forging of Lightbringer.
I dunno, in all likelihood Jon probably is Azor Ahai and he is one and the same as the other two. But I'm in the bargaining stage of grief here.
It's physically impossible for Shireen to die at the same time and place in the books. It's a long way to Castle Black and any progress is going to be slowed by the weather. By the time Stannis next has the opprotunity to see Shireen the Battle for Winterfell will already have been decided as I've pointed out.
So unless Melisandre burns Shireen of her own accord (it's very unlikely Stannis would send a letter ordering it) Shireen won't die to clear up the weather so Stannis can take Winterfell. So a different reason is very likely.
There are two possibilities - either Stannis has already given this order (and his orders in TWOW preview chapter are a ruse), or he loses the Battle of Winterfell.
It's effectively impossible it happens in the books as it did in the show. But I -do- think it's wishful thinking that the broad strokes aren't accurate.