And that American citizen in Yemen is actually sending bombers to kill Americans.<quoted text>
The difference is the shooter in the tower is actively shooting at police or the public. Your terrorist in Yemen's execution was ordered regardless of what activity he may have been engaged in at the time of his execution.
The objective of the police is to subdue and arrest the shooter and protect the public, sometimes there's no other way other than to kill him. Nobody ordered them to execute him before they left the station.
There is no difference.
Both are intent & on & doing harm to innocent people.
Both are unavailable to capture.
Delaying stopping both people would result in more deaths.
When word of that tower gunman hits the SWAT Team, they know exactly what they are to do. If the shooter keeps shooting,they take him out.