Katchen
The big reason to have a zebra-horse hybrid (zorse) or zebra-donkey hybrid (zeedonk) is because zebras are resistant to trypanosomiasis (sleeping sickness) caused by protozoans transmitted by Tsetse fly bites. Horses and donkeys are not. The Southern Roman Empire thread would be perfect for developing and using these hybrids, since they would make carriage by draft animals instead of human bearers possible across the African savannah. (And by the way, the Ubangi, Congo and thence either the Lomani or Kasai and Sankuru Rivers would be a way by boat across the Congo rainforest to the Southern savannah lands--it was how the Bantu got to the Southern savannahs from the Cameroun area they originated in so quickly). Draft animals are very important even if they are not feasible for cavalry. They are not only the difference between walking and riding, they are the difference between crops that can be produced by human beings with hoes and crops that are grown in plowed fields, especially once the moldboard plow is developed. Without something like a zeedonk to pull a plow, Africans must wait for modern self-propelled tractors to get beyond hoed field horticulture as they largely did in OTL.
Zebras cannot be domesticated because they have a complete aversion to anything on their backs. That aversion protects them from lions, enabling them to buck off an attacking lion about half the time (there is a You-Tube showing this) and makes it almost impossible for a horse stallion or jackass to mount a zebra mare (though zebra stallions have no problem mounting more docile mares or jennyasses). It simply takes longer to break down a zebra mare's resistance than a horse stallion has patience so the horse gives up.
Eland (the largest species of antelope) have been domesticated for meat, but whether they could be domesticated as beasts of burden or as milk producers is unknown.
Everyone seems to be forgetting, however, that there is one species in Africa that we know can be domesticated and was domesticated and can be used as beasts of burden in the forest and the savannah and for war as well. I'm speaking of course of the elephant, and yes, African elephants can be domesticated too. The Carthaginians did it, which is why Hannibal was able to take elephants to attack Rome with. So while we might not be able to have horse cavalry for African civilizations, elephantry is a definite possibility.