In the death row case, the capital punishment isn't murder if you use classic definitions. If you change the definitions then it's only murder if you equate all homicide to murder.
And yes, both the will of the people and tradition can justify capital punishment.
That's fair. And in that vein the current killing of the ceo can not rightfully be deemed a murder as no one have been convicted of such.
But then again, the society apparently defines the quality of a killing - only future history will tell if this is a murder, and thst can go back and forth a lot depending on public sentiment.
And yes, both the will of the people and tradition can justify capital punishment.