This is not a death penalty.
The death penalty involved the deliberate execution of a convicted criminal in a controlled situation.
This is a situation where (presumably) a police officer took the decision that the use of lethal force would resolvea situation where a hostage's life was in imminant danger.
The police take these sorts of decisions and act in this way in the UK too.
Here for example
http://news.bbc.co.uk/1/hi/england/london/3726 062.stm
In this particular case the kidnapper survived but that is probably more accident than design!