In the study of historical games there is a strong evidentiary bias towards those that used physical artifacts. A board for ur or a drawing of senet probably predate evidence of a collaborative talking game. Those games have narrative structure, but the state of the game is represented by the placement of physical tokens instead of the use of language.
A major antecedent of role-playing games is divination, fortune telling. The activity can be more or less structured depending on context, but usually involves some kind of spiritual authority and ritual, and possibly introduces new information. All through the history of speech people have been asking each other's advice, and it wasn't far from there to the emergence of trusted elders, shamans, and gurus. Divination rituals include visiting an oracle, throwing knucklebones, consuming entheogens, tarot, and ouija. Some of these are more randomized (i.e. cleromancy) and some are more guided (e.g. séance).
Role-playing games combine the rituals of spiritual authority with the fantasy of board games and the chance of cleromancy. Perhaps the most analogous historical practice --- a guided, collaborative thematic adventure --- is an entheogenic drug trip led by a shaman. Fantasy, suggestibility, and struggle are all present. Archaeological evidence for prehistoric shamanistic trips may be thin, but ethnographic evidence suggests that many peoples brought spiritual drug rituals into the modern age.