I posted some photos earlier. By 1920 there was a strong colonial influence to their architecture not wholly dissimilar to the spanish colonial/island colonial styles favored in hot-weather climates. It's not perfect but more on it than I thought it would be. Also, if you're having them be a modern civilization and have a bunch of huts, it looks rather strange.
If anything, the colonial architecture of Uganda is more similar to the English Caribbean architecture of places such as Jamaica, Barbados, etc. This is of course due to Uganda being part of the British Empire as well as those Caribbean islands. Just look at Mengo Palace, the palace of the kings of Buganda.
The photo you showed has absolutely nothing to do with either colonial architecture and much, much less with Spanish or British colonial architecture. To actually see what Spanish colonial architecture was like, google cities such as Cartagena de Indias, Antigua Guatemala or Quito. Also towns such as Barichara or Villa de Leyva in Colombia.
The photo you show is the vernacular adaptation of "modern" mass produced architecture adapted to the weather, budget and local needs of Uganda. In that picture, all of the buildings have concrete structures and multiple floors.
The Spanish colonial architectrue, as well as Western classical architecture, which includes Republican and Neoclassical styles in Latin America, the USA and Europe, definetely did not use concrete and, when they did in the early 20th century, they never left it expossed to the eye like in the pictures you show.
One of the great "revolutions" and breaks with Classical Architecture made by Modern Architecture was expossing concrete and making it an expressive material instead of hidding it.
I personally wouldn't mind Buganda or the Zulu, having "huts" as their architecture. That's what their cities and towns looked like and that doesn't make them any less "modern" than the people living in London or Paris back in the 19th century. Of course, one would say otherwise if analysing it through the Western-centric idea that progress or modernity is defined by a set of very strict European values. But its about time that Civilization begins to separate from those Western-only ideas of progress. Them living in "huts" is just different, not "less modern".
On the other hand, and I understand that Firaxis might want to portray a different kind of architecture than traditional "huts" for the in-game Modern Era, they might have gone with Modern and Postmodern Ugandan or African architecture in general. Various post-colonial African nations adapted Modern Architecture and reshaped it in ways that better reflect their culture and weather. They could have gone instead with this "style" of architecture to represent a "modern" Uganda or wider Subsaharan Africa.
Some examples of these architecture I'm talking about include, in Uganda, the National Theatre of Kampala and the Namugongo Shire. Elsewhere in Africa you have examples of such architecture in projects like the planned city of Asmara, which is a UNESCO Site, and planned under the principles of Modern Architecture adapted to Africa, with buildings such as the Edna Mariam Cathedral. There's also the Postmodern Basilica of Yamoussoukro. Even works by architect Francis Kere could have been taken into account.
These buildings and proyects from the 20th century could served as inspiration for African Modern Architecture that could have been used in the game if they did not wanted to go with pre-colonial vernacular (or "hut") architecture in the Modern Era.