According to a reporter who was privy to most of the facts, Kyle was being interviewed by an interviewer. And I believe the first person he shot walked up and tried to grab his gun. (***I believe they were fucking with him. Seeing as they knew he was young). He then did a juke move to avoid Rosenberg, backed off and started running.
The guy who was later killed, Rosenberg, then gave chase and threw a bag of something at him as her ran and continued chasing. As the got to the end of the car lot they were in, someone took a shot ( videos of the fire angle seem to suggest it was a warning shot in the air) at this point Rittenhouse turned and fired 4 shots at Rosenberg who had caught up to him.
He then circles around the car. In the videos you see the reporter who had followed the chase, take off his shirt to help the victim.
Kyle comes out of hiding, sees the victim and makes a call that he'd killed someone.
He then started running again, and was chased down, knocked on the back of his head, he trips on himself and falls. On guy drop kicks him but mostly missed and injures himself. Second guy hits him with a skateboard and then grabs and pulls the gun. Rittenhouse gathers and shoots. That's the 2nd fatal victim. 3rd victim had a glock in his hand, froze and raised his hands, then suddenly lurched forward and Kyle takes another shot that rips his bicep.
If the Reporters story is true, then it seems a few 'protesters' were just fucking with him.
***( My opinion)