This is a real commercial for a real board game from 1965, “Mystery Date.”
If you ask me, those girls look a little too young to be going on any date at all, much less a “mystery date.”
An updated version was made in 1972 (to replace all those squares with dudes of the longer-haired vest-wearing variety, I bet). It kept getting updated, adding multicultural boys and other stuff. “Mystery Date 2000,” which I remember, had a fake phone where the dude would call you or something.
And here’s the obligatory shameless parody (click to view fullsize):
The photographer is the main character from Blow-Up, notorious for his treatment of women. John Entwhistle was the extremely talented bassist for the Who. And yeah, I do play bass (and I prob’ly would steal Entwhistle’s bass).