I infer that you argue legal execution is a "zero-sum game" and that as such it stands opposed to your ideal condition, which is rehabilitation of the condemned, both for the sake of that individual and for the sake of society.
I assert that the death penalty is not intended to be a punishment, a deterrent, a service of justice, or a tool for rehabilitation (and it fails in each of these roles). It is a protection. The system of law, policing and incarceration has one goal: the protection of the individual liberties of all persons in a society. Since legal execution ideally is reserved for those criminals who continue to constitute clear and present dangers to the rights of others even when imprisoned, and for whom such a fate would be commensurate with their violations of the rights of others, the death penalty is as far from nihilism as possible: it specifically protects and promotes the freedoms and well-being of everyone who could otherwise be victimized by the condemned. It defends the right to life itself.
So defined, such execution should be rare. As legal execution is practiced, however, it can be used in a misguided fashion. It might be employed in mistaken or corrupt attempts to placate angry mobs; to save resources which would be used for investigation, legal defense, and imprisonment; to justify or conceal corruption; or to propagandize. The fact of these occurrences should not be taken as proof of their legitimacy. The protection of human rights is always paramount, and never to be subordinated to ideas of what is justly deserved, what is punitive, or what is likely to engineer a desired outcome.
The theistic cultures you mention are particularly prone to these errors, because they codify into law precepts of religion, which is proto-philosophy. These precepts are often incompletely or incorrectly justified, and may be based on contradictory logic. Who fails to notice the irony of the religious exhortation to "serve justice" by killing those deemed "deserving" juxtaposed with the bleating condescension that "only God can truly pass judgment." When such philosophical confusions contaminate law and the death penalty is used incorrectly then legal execution can certainly be nihilistic, in the sense that it serves no legitimate purpose, and does not protect the rights of anyone, including the condemned.
Why do theistic cultures engage in nihilistic behavior? Because they hold nihilistic views. Despite much contradictory doctrine about the sanctity and beauty of life, any religious code espousing a reward in the afterlife that trumps life in the here and now, and preaching self-destructive behavior such as self-sacrifice and derision for mortal existence, has as an end result a condition of being anti-life, anti-truth, and anti-humanity.