From 1960-68, the NFL had a 3rd place game. The last one was held after the 1968 season, with Dallas and Minnesota facing each other at the Orange Bowl. Besides being the last Playoff Bowl, it was the last game for Don Meridith. The video below shows the highlights, with some corny footage of coaches and players talking strategy.
The video is also bit gruesome. At the 5 minute mark, it shows Wally Hilgenberg being dragged off the field after sustaining a concussion. Wally would later die from Chronic Traumatic Encephalopathy (CTE). In simple terms, brain damage from too many blows to the head.