This book has touched a large number of disciplines and can have serious implications about the human future, but I'm going to stick to my point about art, media and eventually relating it to gaming and interactive narrative here. I addition to this, I think the book offers a scientific explanation for why we create and love art, and I'll try to touch on this as well.
To briefly describe the book, I'll say it makes a good case for the idea that our human brains have evolved rapidly and particularly about 3,000 years ago there was a big shift. Jaynes discusses how our brains changed around then, allowing the development of consciousness as we think of it today. Previously humans had hallucinated the voices of Gods who told them what to do, much like schizophrenics today (this is bicameralism). As this part of ourselves died out it was replaced over several hundred years by a sense of self, individuality and consciousness. He points at a great volume of convincing material that includes writing, art, music, poetry, religion, iconography, history and the structure of the human brain.
One of the things discussed I personally found interesting is the way it fundamentally changes the way we might understand much of art and its development. He argues convincingly that music, poetry and visual art emerged out of the bicameral mind and remains as a remnant of it. In fact, according to Jaynes, a lot of the art we continue to create is created out of a kind of yearning for what was lost when we changed from a bicameral mentality to a conscious mentality. Music and the poetry of song lyrics still speaks to us much like the voices of the gods spoke to primitive cultures. However, it is part of a yearning and feeling of a lost bicamerality, as opposed to actual bicamerality, that drives a contemporary love for art and music.
Whether this is the original purpose of art is obviously up for discussion, but I think Jaynes' thesis is one that must be taken into account. Assuming he's correct, the purposes of art have surely expanded far beyond beyond a relationship to bicamerality. Art can engage our reasoning facilities, our consciousness, our relationships with others, be a means of education etc. But considering bicamerality and art, even our relationship with art and media today, can be enlightening, especially when you start to consider the cognitive physiology of bicamerality.
I think it would be a worthwhile study to compare what we can assume is bicamerality's influence on art and what we can identify as clearly different from bicamerality. In terms of gaming, it's interesting to note the nature of our metaphorical relationship with characters in games. We might find interesting correlations between non-player characters in video games, the sense of authority that many games exhibit over the game (presumably guiding the player, but this becomes a clear authority over the player) and bicamerality. Further, the ability to inhabit another human character is an act that seems to break with bicameral traditions, and this is one of the more interesting features of many video games. (It was after the breakdown of bicamerality that Greek theatre really took off).
How do we understand participation in the narrative? I might suggest that an ability to actively alter a narrative's outcomes engages our consciousness. However, if our participation is guided (such as the voice of authority mentioned above) does this not suggest a bicameral mentality?