Which is not to say villains aren't capable of redemption. Or that someone who does something bad will always be bad or is bad in all ways. But simply the being the bad guy is more than enough for people to want to see you eliminated.
On the other hand, this sort of thing DOESN'T really adhere to someone running away. If you're off the property and running away, very few people would consider it okay to shoot you. The "righteous violence" only extends to the point where you are actively 'wrong-doing' - it's also why the hero doesn't kill the villain until he draws his weapon.
Although the "villains can redeem themselves" thing is honestly a pretty modern wrinkle, thanks to deconstructive works of film/literature/etc. Incidentally, this is why American popular reaction to things like diplomacy and foreign policy can be so painfully myopic and naive. We want countries to wear hats, and we want those hats to be unambiguous. Britain? White hat (at least in the 20th century). North Korea? Black hat. Japan? White hat now, black hat in WWII.
But yes, as that extends to real-world actions, most people would say that once they're a block or so away from your property, you're probably no longer morally justified in chasing them down. UNLESS they've already committed the crime, and it was heinous. Somebody just raped/killed your wife/daughter/son? I think the property line boundary is out the window. Look at how many revenge films there have been in American cinema (and how popular they are). Charles Bronson made a career playing antiheroes who were committing extrajudicial murder, and people LOVED it. The fact that the legal system is actively trying to prevent him from this is part of the trope. I mean, I realize at some point it just becomes ludicrous (think pulp novels and
Sin City), but there's a very strong undercurrent of righteous violence in American culture. Not only is the good guy allowed to kill, it's kind of a given that he's breaking the rules by doing so and that this is inherently okay.
Not all that surprising that this gets reflected in real life.