Are you sure that was a popular game before TV? Where would they have got the idea? I know those images were not featured in picture books of the early 20th century. Seems to me, the children who played cops & robbers or cowboys and cattle rustlers were imitating the mass entertainment media of their time period: movies and then television. Through these media, they absorbed the values and social organization of their society, long before they were taught formally in school.
As a matter of fact, my friends and I were not playing anything of the sort. We were preoccupied with soccer. We were not even Canadian yet at the age when American [M-designated] children were routinely playing such games. By the age of ten, when I had North American friends, they had outgrown that kind of make-believe. After puberty, I do not believe any "kids" play cowboys, and after 1975 or so, I do not believe the native icon to which I suppose 'indibums' refers was encouraged even among very young children.
There is quite a considerable difference between six-year-olds running around their backyard yelling 'pow, pow' at one another and a post-adolescent sequestered in a dark basement, intensely invested in graphic adult violence in a manufactured electronic fantasy realm, which he may not, but more often does share with virtual assumed personae belonging to unknown fellow fantasists, thus forming a shadow-culture composed of the darker elements of the mainstream one. They develop rituals and secret passwords, icons and symbols and badges of belonging. Whether the medium itself is addictive, the subculture does bear many characteristics of secret fraternities and religious sects.
But there is a consistency in that both media are products of a culture, carry a set of subliminal assumptions and allow the viewer/player to assume - to some degree and for some duration - a role in that social structure other than his own. I don't think that it's practicable for a six-year-old with plastic six-shooter to lose sight of the line between reality and make-believe to the extent that he 'd jump on a horse, gallop to Wyoming and mow down a gang of train-robbers.