Kansas City police spokesman Darin Snapp told NFL Media's Steve Cyphers that the death was being treated as a homicide but no arrests were made.
On Monday, all three persons of interest were released, Snapp said, and the investigation continued.
Here's how Snapp described what happened:
"An individual ... came back to his car, saw someone in his car who did not belong," Snapp said. "A struggle ensued between the two and that's when the person collapsed -- the person that was in the car collapsed. ... We don't know exactly how the person passed away.
"We talked to the doctors, there was no obvious sign of how he passed away -- if he had some kind of medical condition that caused his death, but we do know there was a disturbance between two people," Snapp continued. "One of them is deceased, so we are investigating it as a homicide until we hear differently."
The scuffle ended shortly before 5:20 p.m. with the man unconscious on the pavement, Snapp said. Paramedics administered first aid before the man was taken to a local hospital, where he died. Police identified him Monday as Kyle A. Vanwinkle, 30, of Smithville, Mo.
On Monday, detectives were awaiting autopsy and toxicology results to determine the cause of death.
Chiefs spokesman Ted Crews told NFL Media's Albert Breer: "We're aware of it, but at this point it's a police investigation."
The death came one year to the day after Chiefs linebacker Jovan Belcher killed his girlfriend, Kasandra Perkins, on Dec. 1, 2012, at a home not far from the stadium. Belcher then drove to the team's practice facility and committed suicide in front of then-coach Romeo Crennel and general manager Scott Pioli.
In September 2012, a gunman attacked a Kansas City Royals employee in the same parking lot, which services Kauffman Stadium as well. The gunman shot the employee once in the abdomen and then returned to his vehicle and committed suicide.
The Associated Press contributed to this report.