Of course they do. Most of the western world now understands that two wrongs don't make a right. That someone killing someone doesn't make it right to kill them. That if killing people is wrong unless its in self defense or to protect someone, then the death penalty is wrong.
Why? Because a person in jail is not able to kill another innocent. A violent criminal can be put in a cell by them selves and given limited privileges outside it. In the case of this story, a man shot his girlfriend and now gets the death penalty. His killing of one person is very "eye for an eye" and is likely supported by many christians.
The US Supreme Court has made it official that killing criminals is okay with the constitution now. So lets take a toll. Police tazer old people to death, but tazers are still widely used, even on old people. States can execute criminals for killing others (eye for an eye and two wrongs make a right). The United States Government can spy on its citizens with no warrant simply by calling them a domestic terrorist, which is very loosely defined. The US Government can hold suspected terrorists and domestic terrorists in definitely without charge. The US Government can torture suspected terrorists and domestic terrorists. Its not a wonder the rest of the world hates us. We are who we used to defend the world from. How shameful.