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I think that one very important difference between status games and things that might remind people of status game is how long they are expected to stay in people's memory.
For example, I play pub quizzes and often I am the person who is responsible for the answer sheet. Due to strict time limits, discussion must be as quick as possible, therefore in many situations I (or another person who is responsible for the answer sheet) have to reject an idea a person has came up with based on vague heuristic arguments and usually there is no time for long and elaborate explanations. From the outside, it might look like a status related thing, because I had dismissed a person's opinion without a good explanation. However, the key difference is that this does not stay in your memory. After a minute or two, all these things that might seem related to status are already forgotten. Ideally, people should not even come into picture (because paying attention to anything else but the question is a waste of time) - very often I do not even notice who exactly came up with a correct answer. If people tend to forget or not even pay attention whom a credit should be given, also, if they tend to forget cases where their idea was dismissed in favour of another person's idea. In this situation, small slights that happened because discussion should be as quick as possible are not worth remembering, one can be pretty certain that other people will not remember them either. Also, if "everyone knows" they are to be quickly forgotten, they are not very useful in status games either. If something is forgotten it cannot be not forgiven.
Quite different dynamics arise if people have long memories for small slights and "everyone knows" that people have long memories for them. Short memory made them unimportant and useless for status games, but in the second case where they are important and "everyone knows" they are important, they become useful for social games and therefore a greater proportion of them have might have some status related intentionality behind them and not just be random noise.
Similarly, one might play a board game that might things that look like social games, e.g. backstabbing. However, it is expected that when figures go back to the box, all of that is forgotten.
I think that what differentiates information sharing and social games is which of those are more likely to be remembered and which one of them is likely to be quickly forgotten (and whether or not "everyone knows" which is most likely to forgotten or remembered by others). Of course, different people might remember different things about the same situation and they might be mistaken about what other people remember or forget - that's how a culture clash might look like. On the other hand, the same person might tend to remember different things about different situations, therefore people cannot be neatly divided into different cultures, but at the same time frequency of situations of each type seems to be different for different people.
The pub quiz you play has clearly defined status. You lead it. As such there's not the uncertainty about status that exists in a lot of other social interactions.