Video games are used for a video witch has been changed to a game not to be confused with a made up game like c.o.d or battlefield which is just a game.
The Olympic Games were given their name after Olympia where the games first took place at 776 BCE in order to honour the Olympian God Zeus/ Dias [Ζεύς/ Δίας].
The phrase "called off" usually refers to a game that was canceled before it started. "Called" is usually used when a game that in progress is stopped.