Reddit mentions of Expedition: Being an Account in Words and Artwork of the 2358 A.D. Voyage to Darwin IV

It's called Expedition. I think it's out of print, but copies are available: https://www.amazon.com/gp/aw/d/0894806297/ref=mp_s_a_1_1?ie=UTF8&qid=1510516372&sr=8-1&pi=AC_SX236_SY340_QL65&keywords=Expedition+Barlowe&dpPl=1&dpID=71DAHD99H5L&ref=plSrch

Pure worldbuilding and minimal narrative describes pretty well Expedition and Barlowe's Inferno by Wayne Douglas Barlowe.
Granted, these are books where the framing story (a person exploring the setting in question) is there to provide context for Barlowe's paintings, but you can do pretty much the same thing with words as he does with illustrations- take an explorer, an archaeologist, a historian, or some other sort of researcher, and follow them as they acquire knowledge about the setting. The story will thus focus on their discoveries, rendering exposition and story one and the same.
The SCP Foundation's various exploration logs are the best examples of this that I can name at present, as the characters involved in the framing story are generally anonymous redshirts whose only significance is the strange phenomena they encounter. As far as novels go, I also see the general formula in Jeff Fahy's Fragment.

Another example of an approach that works is the SCP-Foundation. There are traditional narratives on the site, but the main attraction for most of the Foundation's existence has been the collection of fictional documents describing various paranormal phenomena.

A fictional document or fictional documentary strikes me as a perfect method of doing what you seek. You can have an in-universe history book, an in-universe encyclopedia, some other sort of reference work like the Zombie Survival Guide, etc. You could call some of these "stories" by some definition of the word, I guess, but the bottom line is the format and content are quite different from what you typically see in things described as stories.

You like that, you're gonna love this: the book it was based on. Awesome stuff from Wayne Barlowe.

This painting was created for Barlowe’s speculative xenobiology work Expedition. For the Amazon page, please click here:

https://www.amazon.com/Expedition-Account-Artwork-D-Voyage/dp/0894806297

I hope that she gets to do exactly that. Better if im still alive to see it.

Has she ever seen Alien Planet?

There is also a book that inspired the movie. It was considerably cheaper when I bought it.

Wayne Barlowe's book Expedition, the miniseries of which is also available on Youtube here.

"if the stars were gods" by benford and eklund has some imaginative alien life, and at least starts to get at the xenobiological challenge of the anthropic bias - truly alien life could well be so strange and fundamentally different that we won't recognize them as being alive at all, let alone understand anything about their culture. spherical jovian gas whales? you bet. maybe it's because writing stories about humans not noticing that space rocks are actually alive is hard, but i haven't seen this explored that much in scifi.

wayne barlowe does some good work on astrobiological speculation grounded in science: http://www.amazon.com/Expedition-Account-Artwork-Voyage-Darwin/dp/0894806297/ref=pd_sim_b_4

sorry if this is kind of off topic, as you were asking about culture rather than biology. but to me, biology must come before culture, as it's an evolutionary precursor that cannot be circumvented. and if the xenobiological groundwork has been done well, you can well extrapolate that into culture.

It may not be quite what you're looking for, but I always liked Expedition by Wayne Douglas Barlowe.

http://www.amazon.com/Expedition-Account-Artwork-D-Voyage/dp/0894806297/ref=sr_1_1?ie=UTF8&qid=1417873811&sr=8-1&keywords=expedition+barlowe

Reading my 4-year-old son Expedition, which is probably my favorite book of all time. I thought it might be a bit too old for him but he seems really into it.