While I agree, it was probably not a "wise" decision to be there, Kyle had just as much right to be there as any of the other people that night. Perhaps more, because he was there by invite-by-proxy to protect the car lot.
The first shooting was justified, in my opinion and that of the 12 jurors, because Rosenbaum had earlier threatened to kill Kyle if he caught him alone. After Kyle put out the dumpster fire, Rosenbaum, who was walking ahead of Kyle, ducked behind a truck and waited in ambush. As Kyle passed him he started chasing Kyle, his friend fired a shot in the air - prompting Kyle to turn around. Kyle was then cornered in the back of the parking lot, Rosenbaum yelled "fuck you" and lunged forward reaching for Kyle's gun. At that point in time, Kyle shot him 4 times (including the "once in the back" only because Rosenbaum fell forward as the last shot was fired - not because his back was turned.) I'm not sure how you can be more justified than that.