I had this Battleship game as a kid in the early 70s and remember thinking the cover illustration was weird. It showed Dad and Junior having the time of their lives playing the game as Mom and Lil Sis watch the action while scrubbing dishes and smiling approvingly at the menfolk's pleasure. Why did Milton Bradley feel the need to show the mother and daughter in the illustration? Eventually, the game company replaced the illo with a photo of a boy and girl playing the game.
Over at HiLoBrow, Lynn Peril writes about this Battlefield cover, putting it into context with many other ads of the era that depicted "girls and women sitting on the sidelines while they watched boys and men doing things."
Sometimes a girl watched her brother do things, like play the organ, shoot a pellet gun inside the house, or blow up an incredibly phallic balloon. Sometimes, as in a very odd ad that appeared in a 19__ issue of Boy's Life, a girl watches a boy who watches birds while holding a typewriter on his lap. Something about her mild leer suggests he is not her brother.
If girls and women played games and sports with boys and men, the consensus opinion of most dating experts was that nothing killed a budding relationship faster than performing better than one's date (assuming, as always in the mid-twentieth century, that everyone either was a cis-gendered heterosexual or aspired to be). "This is definitely not the time to put on an exhibition or give him a lesson, no matter how good you are," advised Datebook's Complete Guide to Dating (1960) in a chapter on "Active Sports Dates. "If you show off and show him up, you'll strike out permanently…. Never come on like a pro."