I am interpreting this to mean that there is no Scramble for Africa. But France has Algeria, and British have a protectorate in Egypt after Ismail Pasha's bankruptcy. The Capetown colony also exists, and the Portuguese have coastal settlements in Angola and Mozambique. There is a scattering of forts and such in West Africa and elsewhere. Let's say that despite the potential resources, Africa is seen as too poor with too many health problems to make it worth their while. European involvement in Africa remains limited to local entrepot trading and various scientific expeditions.
So what does the rest of sub-Saharan Africa do on its own? Not a whole lot. The indigenous empires will continue to exist, waging war, capturing slaves for their internal use, expanding their domains, etc. Slowly, such states will be incorporated into the international diplomatic system, but likely only after they achieve a certain level of institutional development, power, and adhere to certain European standards (like abolition of slavery).
Political development will be slow in coming, but may happen as Africans study in Europe and learn about European politics. But liberal reforms will be almost impossible at this stage. We won't see any significant changes for decades.
Their economies will remain very undeveloped. No railroads will be built. Resource extraction without European capital and technology will remain limited. While there are other commodities (certain agricultural products, tropical woods, ivory) that can be exchanged, they will become less and less important to the world economy. In most ways, Africa will be economically worse off although any surplus will be consumed by African elites instead of Europeans.
Of course, European businessmen may still try to work with the local governments to scout for resources, build plantations, and perhaps even introduce some very local infrastructure to allow transportation of mined or plantation goods. Such investments will be limited, as the goods must be of very high value and quickly extracted to justify such a high risk of investment. The local kings might just decided to seize control of it. But there are several places where that might be worthwhile, especially in South Africa.
Eventually, as African elites interact more with Europe and other parts of the world through trade and intercultural exchange, they will see how undeveloped they are. Their efforts to "modernize" their kingdoms and empires will meet with varying success as indigenous cultural elites will both see opportunities and threats to their own power.
Most African lands continue to be affected by changing weather conditions (drought in the Sahel for example), and population shortages due to disease and habitat. Despite the incorporation of new technology and goods from trade, they are unlikely to ever achieve enough capital surplus for any kind of capital development which is necessary for non-Malthusian growth.
The most we might see is several states similar to Ethiopia in the 20th Century in terms of its political and economic development. There might be such states based around the Niger River, Lake Chad, Swahili East Coast, the Congo, and Natal. These states will be increasingly prone to internal disruption and revolution as local elites see traditional politics as a reason for why they are so undeveloped compared to Europe and the rest of the world. Local revolutions and coups might happen in the 1970s especially under local conditions of stress caused by environmental factors like drought.
Other than different borders and more pronounced cultural distinctness, I don't see too many differences between such an Africa and they one we have. It's just that with local socities being kept intact that there would be a significant local elite. That may provide more stability, but it would also retard innovation.
