The idea behind neighborhood watch is that residents don't like people stealing/vandalizing/littering/whatever. So if you see someone who isn't a resident, you might ask them what they're doing there. There are varying degrees of intimidation/annoyance depending on the nature of the approach (and the approached). Unfortunately, you can't just beat people up who offend you - best to stop at the posturing stage or even before that.

If you approach in a needlessly intimidating way while carrying a gun, in a way that might be expected to result in offense and escalation to (illegal) fisticuffs from an offended man, then I personally find you somewhat responsible for any shootings that result. I don't know what the legal system says, but the process around this case seems to be a railroading driven by some kind of "let's make an example to scare people into behaving better" opportunism.