The item use game had several rounds, so I think it would be more appropriate to compare a single round of the item use game to the single round of 20 questions. As a mentioned before, people tended to shout out random answers, which were seized upon and refined by other players if the response from the owner of the item seemed favorable. In this situation, players competed against each other and the owner of the item played a much less dynamic role than in the case of Shipka and the pickle relish. The protagonist would be whoever finally guessed the correct usage of the item - even if their ideas had built off of the ideas of others. So there was still some cooperative element in building off others, but it was to a much lesser degree and there was little conference among players. However, there were ways of gaining status within the game other than a correct guess - some players had the advantage of knowing more people in the class, and therefore were more likely to know the owner's history that could relate to the item. These players became central nodes of the narrative, and tended to speak more. Another method of "winning" was to come up with clever or amusing answers, even if they were completely wrong. So, I think we might remember more key players from that game, as there were more ways to "win."
Just a thought - I wonder if the item use game narrative would have progressed more like the 20 questions narrative if played by members of a more collectivistic group? (For instance, a group of close friends.) In a school setting, our default reaction to any challenge is likely competitive, focused on goals and power, whereas in a friendlier setting we may tend to seek approval and resources from our in-group. The tighter constraints of 20 questions in essence transformed our class into a collective "us" vs. "them" so individual competition was redirected.
I’m sure we’ve all experienced group work in which there was not as much cohesion, though - probably because loose constraints do not sufficiently motivate most people to set aside individual ambition. Student narratives that examine group dynamics, such as evaluations of class partners, often focus on the personal qualities and faults of fellow members while ignoring how the “obvious” constraints of the task (time, materials, etc). The same thing goes for the “blue sheet” student evaluations of teachers - perhaps a lecture teacher who seemed boring was constrained by the time limit of the class, or something like that - but there’s a tendency to assign oversimplified “protagonist” and “antagonist” labels, losing the people, conditions and events that shaped the main characters.