I'm between two choices:
1.) theoretical definition: this type of definition attempts to provide an adequate understanding of the thing(s) to which the term applies.
I think this because murder is the killing of a human by another human and the death penalty is, by lexical definition, sanctioned by the state.
2.) persuasive definition: this type of definition is a definition that is slanted (or biased) in favor of a particular conclusion or point of view.
I can see the merit of this viewpoint, because murder has a negative connotation and the "air quotes" indicates that the speaker does not consider the death penalty to be a truly valid or straightforward term.
While I personally believe this definition is theoretical, I also believe that I am just thinking to hard and maybe a little too literally/unemotionally. What do you think?
EDIT: the lexical definition of murder also stipulates that it is "pre-meditated" (check) and "unlawful" (this part is over-ridden by the addition of the state sanctioned attribute.