It does seem like a lot. I assume that the intent was to make it large enough to viably support a shadowrunning scene?
But on the suspension of disbelief side, sure, on the one hand it has about 60 years of being the capital, and that will draw in people. But on the other hand Ottawa-Gatineau has almost 160 years of being the capital of Canada (national population about 40 million now) and it has about half of that population. I guess in the Sioux Nation there isn't as much competition from larger cities already existing.
Or to look at something maybe more comparable, Taiwan had a huge population inflow following the KMT withdrawal to there after losing the Chinese civil war about 80 years ago, and the island population has grown substantially since then too, going from around 7.5 million in 1950 to about 24 million now. So it is a country that had to urbanize quickly and build a lot of housing, etc, even more than the Sioux. The capital, Taipei, is now about 2.6 million but the greater sprawl is about 7.5 million. So about a third of the population, and about equal to the population of the country 70 years ago.
So now I'm maybe convincing myself that the Cheyenne numbers are not entirely crazy, assuming:
- There was a lot of immigration into the Sioux Nation (between people with thin claims to tribal blood, people from other NAN countries thinking life would be better in the Sioux nation, metahumans who were accepted, etc.)
- The Sioux government chose to build much of the needed housing in Cheyenne. Likely either government owned building projects or sweet government contracts to mega-corps or giving sweet concessions to mega-corps to develop certain resources provided they also provided housing for the employees and extended families in Cheyenne
- A lot of high density, cheaper to build, housing. A lot of apartment blocks or something like that. Land they have, but there is a cost to every wall so either people likely have to live quite communally or a lot of apartment buildings were built, because there just would not have been the capital to make that many house.