I'm guessing you haven't reviewed the evidence and are relying on news accounts? I'm only saying that because the evidence isn't being covered in the news, it's not an insult of any kind.
This is what the forensic evidence, Wilson's testimony, and credible witness testimony describes:
Wilson heard about the robbery while on a call helping a sick child. He offered to assist. He was given a description of Brown. He then saw Brown in the Road with Johnson. He told them to leave the road. They refused. He had driven past but realised Brown fit the description and had the cigars. He called for assistance. (all supported by radio call recordings and credible witness accounts). He backed up and attempted to get out.
Brown slammed his car door (supported by a palm print on door and credible witnesses). Brown started assaulting him (supported by Wilson's injuries, credible witnesses, and DNA in the vehicle). Wilson and Brown went for his gun (supported by DNA on the gun, two shots fired into the car, a wound on Brown's hand from the second shot, Brown's blood in car). Brown ran after he was shot and Wilson exited his car and pursued. Brown stopped, turned, and came at Wilson (supported by blood trail, credible witnesses, wounds). Wilson called out loudly and repeatedly to stop and get on the ground (according to witnesses including Brown's friend). Brown kept coming so Wilson opened fire while back pedaling (supported by where the casings were found and credible witnesses). Wilson paused shooting after he knew Brown was hit to give him a chance to surrender while calling out to stop and get down (supported by audio recording, casings locations and credible witnesses). Brown kept coming at Wilson and Wilson kept retreating (supported by blood trail, credible witnesses, and shell casings). Wilson opened fire again delivering the fatal shot when Brown reached 8' away. Brown stopped and Wilson stopped firing with one bullet left.
So, I disagree with your assessment that non-lethal force would have worked. 8' from fighting for his life again with a 6'5" 290 LB man and one bullet left.
And no, the presence or lack thereof of a weapon isn't necessary for self defense. Wilson had a reasonable belief he was in danger of great bodily harm or death if he didn't stop Brown from charging. Wilson is a cop. He was pursuing Brown because A) Obviously, it was his job to pursue a felon and protect any more victims and B) According to Wilson, He wanted to keep him in sight until his backup arrived which he knew was very close.