So if you rush to gun down someone with people shouting "he killed! get him!" that's perfectly fine in your opinion? (because why else would you pull a gun)
Do you honestly see lunging at someone with a gun as attempt for de-escalation rather then escalating it further?There isn't a comparison here. Your fixation on making Gaige sound just as guilty as Kyle is flat out ridiculous at this point, the situation was already escalated BY Kyle, he was being chased because he killed someone.
Do you seriously expect for Kyle to just lay down and accept being potentially gunned down, with gun right in front of his face, while calls to kill him are heard around?
They aren't talking, Kyle cannot run as he is sitting on the ground, there is less then half a second to decide wherever to shoot or not.
If you go with "who started" then situation was initially escalated by Rosenbaum, the rest flew from there.