I think that the first psychologist to suggest that fiction originates in play was Sigmund Freud. In 1908 he published an article in a Berlin literary magazine, entitled Der dichter und das phantasieren (Creative writing and day-dreaming). It starts like this:
We laymen have always been intensely curious to know ... from what sources that strange being, the creative writer, draws his material, and how he manages to make such an impression on us with it and to arouse in us emotions of which, perhaps, we had not even thought ourselves capable (p. 131).The secret? It’s that the writer draws on the play of childhood, and on day-dreaming which is one of its adult continuations. In play, says Freud, children act out their wishes: of being grown up. Day-dreaming and night dreaming, Freud asserts, are also expressions of intense wishes. Writers—especially popular writers—offer such dreams which are typically of either (as Freud puts it in a slightly stuffy way) an ambitious or erotic kind. He uses these terms to indicate the motivations of what we now call action stories (liked mainly by men) and romances (liked mainly by women). He points out that in an action story a hero may lie “unconscious and bleeding from severe wounds” at the end of one chapter and find himself, at the beginning of the next chapter, being “carefully nursed and on the way to recovery.” One reads such stories with a sense of security. They are of what we wish for ourselves, to succeed in a grand way despite all adversity, and to be tenderly cared for. In raw form such phantasies in adulthood would seem too infantile for us to admit to others or even to our selves. Creative writers transmute such ideas into something acceptable.
A year earlier Freud had published his first work on fiction: Delusions and dreams in Jensen's Gradiva. In it he analyzes Norbert Hanhold, a fictional archaeologist who is the protagonist of Wilhelm Jensen's 1903 novel, Gradiva. In the story Hanhold obtains a copy of a Roman bas relief of a walking woman in a flowing garment, and starts to experience compelling phantasies and dreams about her … (Freud himself acquired a copy of this same bas relief in 1907, and it is still on the wall of his room in the London house where he died, now a museum.)
Freud points out that play in childhood is a source of intense pleasure. We don't give up such pleasures, Freud asserts, we exchange their sources for something else. So as play declines towards the end of childhood, it's exchanged for other things, equally pleasurable, that derive from it, such as fiction.
Brian Boyd (2009). On the origin of stories. Cambridge, MA: Harvard University Press.
Sigmund Freud (1907). Delusions and dreams in Jensen's Gradiva. In A. Dickson (Ed.), Pelican Freud Library, 14: Art and literature (pp. 29-118). London: Penguin (current edition 1985).
Sigmund Freud (1908). Creative writers and day-dreaming. In A. Dickson (Ed.), Pelican Freud Library, 14: Art and literature (pp. 130-141). London: Penguin (current edition 1985).