Institutionalized murder.
Equating execution and murder is fundamentally flawed. By your definition, the legal incarnation of a criminal could be construed as institutionalized kidnapping or the legal taking of property to pay off debt could be interpreted as institutionalized theft.
The legal incarnation of a criminal is institutionalized kidnapping. That's what the "state monopoly of [insert correct English expression here, the German one, Gewalt, may mean power or force or violence]" is all about: Citizens have abdicated the right to do these things to the state.
What's wrong with the Gurl's phrase is that it doesn't say that not even the state should be allowed to take somebody's life, especially since the decision will, in the end, be up to individuals - more or less just like in ordinary homicides.