Humans apply taxonomy to nature, useful but ultimately flawed models.
Reality seems to be continuum, nature does whatever works and has no concern for neat categories.
My opinion is viruses are "alive" as they are unique replicating and evolving genetic code that can be identified distinctly from the host.
Other opinions are they must have other biological process to be considered "alive". The debate does not seem to be settled, its pretty similar to the is Pluto a planet, again another human taxonomy that not everything in nature fits neatly into.
I think as we discover more of the universe our definition of life will probably need to evolve. Already our computers make us question the definition, when will software become "alive" or "conscious". We already sometimes speak in terms of "biological" or "organic" based life.
Sorry this really doesn't answer your question, but "inactivate" is probably more accurate than "kill."
Alive is just a word. It means different things to different people and any formal definition will necessarily be arbitrary.