I am going to assume you are referring to a human, not alien, society.
Human societies are extremely diverse. One glaring example is the urban-rural divide. This divide alters the opportunities for social interaction. Isolated sparsely populated rural communities have very few institutions that allow for social interaction, beyond religious centers and the local store. The economics does not support large social venues. Thus, people in isolated rural communities would live the lifestyle of your introvert society.
On the other hand, densely populated cities force people to closely interact and to come together in large groups. Consider just the educational system - single-room schools vs hundreds, if not thousands, of students.
There are also clear distinctions between people living in densely populated apartment buildings vs suburbia. Research indicates that suburban neighbors are much more interactive with each other than are inhabitants of high rises. High rise living tends to produce introverted behavioral interactions (compare how people interact in elevators vs how they interact over the back-yard fence). There are anecdotes about people meeting in bars who have lived in the same building for years, but never interacted.
There are cultural differences, as well. Japan, for instance, puts a high premium on privacy, in spite of a densely packed population. Japanese culture has developed the ability to be alone in a crowded room. Boundaries become very important, and violating these boundaries is heavily socially sanctioned. One can be in a very crowded train, and still be alone. Isolation pods at airports are common in Japan, and catching on elsewhere. See Italy's ultra-cheap airport 'capsule hotel' lets you sleep in a pod while you wait for your plane for an example.
So how many of the differences between introverts and extroverts are the result of a genetic vs an environmental/cultural determination? How much of human behavior and attitude is driven because the people are living in cities, vs how much influence does living in a city have on human behavior?
However, high-functioning autism IS a genetic characteristic. There are notable differences in how autistic people respond in social situations. They, in point of fact, do require periods of quiet time. It is not so much a distinction on a generalized introvert-extrovert trait, but on a very specific wiring of the brain related to the perception of social situations and social cues. Thus, the answer is not conjectural, but observable.
If the ratio of autistics to neurotypicals was reversed, and autistics became the norm, there would be radical social changes on society. Perhaps this is more specific to your question, so I posit your answer can be found by regarding the preferred environment of the high functioning autistic. It would be synonymous with your introvert-extrovert division, but would be neurologically supported.
So, perhaps looking at a well-defined and studied group - those with Asperger's - would be a good starting point to answer your question based on sound medical and psychological science.
I would suggest that entertainment venues would be the most radically effected, as they tend to be voluntary activities. That is, there is no compelling reason to attend entertainment institutions. We have already seen the demise of the movie theater, as private and personal media has become common. People are curling up in front of large screen televisions with surround sound, leaving movie theaters to a particular dwindling segment of the population. Virtual reality is, by definition, isolationist in nature. The participant is locking out the real world. Autistics prefer such personal entertainment venues, rather than more public venues. Public venues that provide strong privacy boundaries, such as seating in a public environment where the seats are distinctly separated, might survive. It is also my experience that huge sports venues would be poorly attended. The crowding on entering and exiting would be the main impediment, as are the line-ups for food. If the seats were individual, with arm rests, as opposed to bench seating, perhaps. But even these types of seats produce discomfort in autistics.
On-line shopping is another trend that would become common. This societal change, especially over the busy Christmas season, is well suited for the autistic. I suggest that there would be few bricks-and-mortar stores in your community. Modern technology would enhance the formation of such a community. In fact, one could posit that our modern technological society is tending to such a non-social environment.
But social interactions would not cease entirely. They would change in nature, but they would still exist. Interactions would be far more personal, and based on specific tasks, less based on the necessities for social niceties and talking just for the sake of talking. Saying 'hello' would be done as a means to announce your presence, rather than any social convenience or requirement. The traditional initial 'How are you?' greeting would simply vanish, as being purely superfluous speech, as opposed to task-specific communications.
Facebook and twitter would become less social media, and more information dispersal media.
Edit
In researching a biological basis for introversion, I came across the following article. Will the Real Introverts Please Stand Up?.
It posits, towards the end, in the section titled
The Engine Behind Extraversion-Introversion
that variations in dopamine response may be a biological determinant of introversion.
This probably explains why a lot of introverts notice that they often
need to be alone to recharge their batteries after vigorous social
interactions, whereas extraverts appear to gain energy from social
interactions. This can be explained by dopamine's function in
energizing potentially rewarding social interactions, as well as its
role in overcoming the cost of effort. For introvert's, such
interactions are more effortful and tiring due to their less active
reward system [5].
However, the article also emphasizes that actually identifying what constitutes introversion is extremely controversial, with a wide variety of interpretations. There are 'check lists' galore that are applied, some completely contradictory. So I posit that unless and until the determination of what is called 'introversion' has some biological basis, such as autism or dopamine response, instead of a vague 'personality' or 'behavioral' basis, trying to define an introverted society will be like nailing jelly to a tree.
