I've come up with two alternative civilization classification systems.
One is the idea that through advances in efficiencies, nano-machines, bio-engineering, a civilization's galactic footprint actually shrinks until the casual observer would see a primitive society where it was actually quite advanced -- wizards would be a big clue though.
I believe there is a non-trivial body of evidence that previous civilizations along such lines may well have evolved before our own. I'm not sure what you'd label such a civilization but I do believe there are many ways of knowing and many ways of evolving and that a more spiritual inward directed civilization might tend to evolve in this manner.
The other is connected to extra-terrestrial communications within Einsteinian limits and societal stability. How much would we have to change in order to have a conversation that spanned lifetimes? What questions would you ask, knowing that only your grand-children would get the answer?
What about an answer to a question that had been asked a century ago? And how would such a conversation affect your outlook on everything else?
This might be plausible in the type of civilization you speculate upon above. You would need to have a connectedness between people and generations that just doesn't exist in our present day society.