He's fast enough to move his body and arms to deflect all the incoming bullets from a weapon that shoots some 700 shots per minute, which means he can reposition his light saber 12 times a second, precisely. That takes some godly speed, assist lines or not. So, with such speed available, I don't think Death Gun would have had much time. Enough time to shoot Pale Dude, sure, but only if he wanted to drop all the theatrics afterwards. If you are correct and DG aims to publicly execute people, then he absolutely needs those dramatic moments. If Sinon had kept shooting, forcing DG to keep dodging, making it impossible to shoot somebody so calmly and cold-bloodedly, and Kirito had been speeding down the hill, he might have wanted to wait for a better opportunity to get his message through.
Now Kirito gave the terrorist all the time he needed not only to slay Pale Dude in peace but also to deliver the performance and then disappear. In fact dodging the single sniper shot kind of made him look ever tougher and more skillful, and thus frightening to those who are starting to fear he's really killing people.
One could enter the tournament with any nick they wanted, so the government would have absolutely needed the company's help to pinpoint any player getting shot and link it to the real account name. The company wouldn't have complied easily, with accusations being so absurd at a first glance. So absurd that the government dude needed to hire a school boy like Kirito to do the actual detective work, as nobody else would.