In the Americas you would have had the Thylacasmilidae (I probably spelled that atrociously), which were sabre-toothlike marsupials, and later on members of the family Felidae such as Eusmilus and the more famous Smilodon. In Africa you would have had Megatereon (an early sabre-tooth, sometimes called a dirk-tooth) and Homotherium (which was also called a scimitar-toothed cat, having more curved teeth than more traditional sabre-toothed cats did). So loosely speaking, you would have had “sabre-toothed” cats in Africa.
Not all of these would have been around 5 to 7 million years ago, though, the time that the article is focusing on. The Thylacosmilidae would have been around in South America, as would Megantareon in Africa. Eusmilus would have been long gone (they were from the Oligocene epoch), and Homotherium probably not around yet (they appeared in the early Pliocene). Smilodon was still a long way in the future (late Pliocene).
And reading back over my post, I see that my spelling is rather erratic, but I don’t feel like spending a lot of time searching around online trying to figure out the proper spelling of each of those names.