How about the UK game show, "The Generation Game"? Bruce Forsyth sang the theme song titled "Life is the Name of the Game".
"Chain Letters", another UK game, had lyrics to its theme song. In viewing the opening on TV Ark, the singers helped explain the concept of the game as the show was starting...
"Take a word. ["CHOIR" is on the screen]
Change a letter. [O becomes A for "CHAIR"]
Do it again. [R becomes N for "CHAIN"]
And you've got a chain. [add "Letters" to "CHAIN"]
That's how you play Chain Letters, Chain Letters."