To be fair, it took us protestants a while to fix that too.

Isn’t the pope basically the president of the vatican? Who else would or should someone carrying out a death penalty report to?

It's a monarchy, yes (technically a 'personal prelacy'). He calls himself the "supreme pontiff" (bridge) between heaven and earth--yet that role is reserved to Christ Alone. He calls himself the "vicar" (the 'instead') of Christ--yet that role is reserved to the Holy Spirit. The greek word for 'instead of' is 'anti-' -- thus, "he is that antichrist." The church is not to handle civil matters, especially not corporal punishment. She "bears not the sword." The power to judge a man worthy of death, and to execute it, is given to humans as a whole. This is why we have the trial by jury. See Genesis 9:6.