The firefight occured on Oct. 17 in the city of Culiacán. Security forces were able to capture Chapo's son Ovidio Guzmán López but ultimately released him after cartel members began attacking civilians and burning nearby buildings.
In the video, Guzmán López is seen surrounded by police and urging his brother to call off the fighters.
"I've turned myself in," he said to Iván Archivaldo Guzmán Salazar. "I don't want there to be riots."
Iván refused and the fighting continued until a deal was made to trade Ovidio for several captured police officers.
Mexican President Andres Manuel Lopez Obrador backed the decision of police on the ground. In a press conference, he said the danger to civilians was too great.
"They made decisions that I support, that I endorse, because the situation became very difficult and many citizens, many people, many human beings, were at risk. And, it was decided to protect people's lives. I agreed with that because it's not about massacres -- that is over," Obrador said. "They (local authorities) took that decision and I supported it."
He continued, seemingly pointing toward a future plan to avoid these sorts of dangerous confrontations.
"The war was not waged. The confrontation and the life of the people was taken care of. It is the most valuable, the most important, the sacred. Don't risk anyone's life," Obrador said. "It is no longer to face violence with violence, evil with evil. There is no war against drug trafficking. We will not expose the lives of civilians with the euphemism of collateral damage. That is over. We want peace and as we have said, it is the fruit of justice. Here it is a new security paradigm."