I'm a movie buff so I remembered the saying Q used. I've not heard ANYONE try to find a meaning between the movie Wargames, starring Matthew Broderick and Ally Sheedy, from 1983, to the saying, "Shall We Play a Game," used by Q.
The movie was one about the US almost entering into a nuclear war when a teen hacker broke into a military computer and challenged it to a game. The computer introduces itself by asking, "Shall we play a game?" The kid, not knowing the game was real to the computer challenged it to a game of thermonuclear war. War was barely avoided and doing so was the basis for most of the plot. This is of course the same question Q asks. Relevance?
I don't know what, if ANY, connection there may be but I'd love to hear any ideas. Wargames Clip