From 1960 through 1966, the teams that finished second in the NFL East and West divisions hooked up for a "consolation" prize...3rd place. From 1967, the teams that lost the East and West Conference championship games, played for third place.
While the game didn't bring in a lot of excitement, the players on the teams earned a bonus for the game (and with the salaries at that time, bonus money was more important).
I read an article the other day about all the complaints made by members of the 49ers and Patriots after both lost their championship games. The writer, probably unfamiliar with the legacy Playoff Bowl, suggested the two teams hook up and play a 3rd place game called, "The Whiner Bowl." Quite interesting.
The legacy Playoff Bowl ended after the 1969 season when the AFL and NFL merged into one league. The AFL never had a Playoff Bowl.
The last one took place after the 1969, season, when the L.A. Rams pasted the Cowboys 31-0.
January 7, 1961- Detroit Lions 17, Cleveland Browns 16
January 6, 1962- Detroit Lions 38, Philadelphia Eagles 10
January 6, 1963- Detroit Lions 17, Pittsburgh Steelers 10
January 5, 1964- Green Bay Packers 43, Cleveland Browns 20
January 4, 1965- St. Louis Cardinals 24, Green Bay Packers 17
January 9, 1966- Baltimore Colts 35, Dallas Cowboys 3
January 8, 1967- Baltimore Colts 20, Philadelphia Eagles 14
January 7, 1968- Los Angeles Rams 30, Cleveland Browns 6
January 5, 1969- Dallas Cowboys 17, Minnesota Vikings 13
January 3, 1970- Los Angeles Rams 31, Dallas Cowboys 0