Capital punishment is not murder. Even killing millions of innocent people, like the US likes to do for financial and racial reasons, is not technically a murder.
I think they were referring to the fact that the state has the monopoly of violence: it is the only moral agent, in the country, with the right to kill without making it a crime.
So it's a murder "technically physically" but not "technically legally".
PS: I'm not endorsing death penalty in anyway. I oppose death penalty.
Murder has a meaning that predates legal definitions.
Also, many groups in history are currently accused of murder despite it being legal at the time.
From slave owners to Nazis, from communists to African warlords.
They committed genocide. Even worse, obviously, but it fits the definition of word “genocide” better than “murder”, thus I believe we should be using that word instead.
Okay, let’s use another example. Is software piracy stealing? Some people claim it is. I don’t, because words have meanings.