It is insane to shoot a taxi driver for giving you the wrong change. It is not insane to shoot in self-defense someone robbing you for $12k. Unless you are so anti-gun as to argue that self-defense is never justified and we should just roll over and let ourselves be robbed/kidnapped/murdered, but then I'd say it is you who are insane. Even in my liberal guns-practically-banned state, shooting and killing a robber is perfectly legal (NY PEN 35.15 2b). Here, a robber doesn't even need to explicitly threaten to use deadly force against you first - being in a robbery is specifically listed among a few select crimes automatically considered to be a life-or-death situation. You can also, even as a non-police officer, use force to detain a criminal or to prevent escape from custody, which is the situation that happened in the article.
Under the law, you have to shoot or detain the right person though. You not only have to think they are guilty, and not only does your thought process have to be reasonable, they have to also actually for real be guilty. If you kill an innocent, you are liable for murder. If you arrest an innocent, you are liable for kidnapping. That's what the court trial is there to determine. The old man failed on the latter two requirements and was justifiably found guilty. A police officer has an additional qualified immunity. They can arrest someone who they think is guilty, and not get in trouble if the person turns out to be innocent. As far as I understand it, legally this is the only distinction between a police officer and a private citizen in US law.
Also, neither a police officer nor a private citizen can use deadly force to prevent escape (other than a few special cases, like in prisons). That's another strike against the old man. If a police officer had shot the courier trying to walk away like that, they too would be (or ought to!) put on trial for murder, as that's not covered by qualified immunity. Like in the example of that guy who got killed on video in 2015 while trying to walk away from a traffic stop.