It's been more than a decade since I have read it, but I remember Diamond writing specifically about the relative lack of domesticable animals in sub-Saharan Africa. Mali, Songhai, and Oyo didn't "[adapt] horses to tropical conditions", they imported already domesticated animals from elsewhere (North Africa). It is telling that none of your examples are in Central or Southern Africa.

Also, domestication is the process of breeding animals over multiple generations to make them more pliable and is not the same as training individual animals to pull a carriage. The very first sentence of the paragraph that you quoted from the Wikipedia article on zebras is "Attempts to domesticate zebras were largely unsuccessful."