I see you're posting moved through the servers at the University of Maryland - hardly a repository of "code of the west" knowledge. Nevertheless, assuming you are trying to increase your store of wild west lore, let me disabuse you of what you hope to be the case:
Here's one example:
"Texas Penal Code 9.42 DEADLY FORCE TO PROTECT PROPERTY"
"A person is justified in using deadly force against another to protect land or tangible, moveable property: (2) when and to the degree he reasonably believes the deadly force is immediately necessary: (A) to prevent the other's imminent commission of arson, burglary, robbery, aggravated robbery, theft during the nighttime, or criminal mischief during the nighttime, or (B) to prevent the other who is fleeing immediately after committing burglary, robbery..., and (3) he reasonably believes that (A) the land or property cannot be protected or recovered by any other means, or (B) the use of force other than deadly force to protect or recover the land or property would expose the actor to... risk of death or serious bodily injury."
In the Joe Horn case, the two goblins had just committed a burglary and were fleeing, thereby fulfilling (2)(B) above. Joe is in his 60's and the two squints were young, strapping males. Even if Joe could catch them in a foot race, and even if they were unarmed (the weren't - they had pry-bars and other burglar tools) the chance of death or serious bodily injury is a reasonable expectation, thereby meeting the requirements of (3)(B).
So, Joe simply sicced old double-barreled Betsy on their asses.
I'm sure Joe didn't have a Texas Penal Code checklist on hand so he could mark off the nuanced requirements of the law.
He simply saw his duty and he did it.