The Mating Game or Red and The Bodyguard ? (5)
I believe the answer is:
chess
'the mating game' is the definition.
(as in checkmate)
'red and the bodyguard ?' is the wordplay.
'red' becomes 'Che' (Che Guevara the Marxist revolutionary).
'and' means one lot of letters go next to another.
'the bodyguard ?' becomes 'ss' (the SS was originally Hitler's personal bodyguard).
'che'+'ss'='CHESS'
'or' acts as a link.
(Other definitions for chess that I've seen before include "Board game for two players" , "Pure-skill board game" , "Musical - board game" , "A game of skill" , "Game with kings and queens" .)