Left to right: A. giganteus hunting Chilotherium, A. horrbilis hunting giraffid, A. kabir having caught a Sahelanthropus, and A. coloradensis hunting Teleoceras.
By the Late Miocene, around 11 million years ago, cats first rose to the position of apex predators across much of the globe (sans Australia and South America). These weren’t the familiar felines and panthers of today but the extinct machairodontines, the saber-toothed cats. The group that saw by far the most success were the scimitar cats (homotherins) and long before the emergence of the long-limbed, cursorial Homotherium (Pliocene-Pleistocene), more generalized but significantly larger forms ran rampant across much of the world around 9.5 to 5 mya. The taxonomy of early scimitar cats is notoriously messy, with the genera Machairodus, Amphimachairodus and the exclusively North American Nimravides having joint custody of various species respectively, but many of the largest species have been assigned to Amphimachairodus in recent years, with the generally accepted species dating to between 9.5 to 5 mya, while Machairodus has been cut down to a few Old World species dating to 12.6 to 8.7 mya.
What's notable about the many species of Amphimachairodus is their penchant for gigantic sizes, comparable to Smilodon populator, which include A. giganteus from Eurasia, A. horribilis from China and A. kabir from Chad, and even smaller forms like the North American A. coloradensis were still around the size of modern tigers or lions. The skull of A. horribilis is 16 inches long, only rivaled in size by the largest S. populator, while A. giganteus shows marked sexual dimorphism akin to modern big cats, which could perhaps indicate lion-like social structures (though solitary big cats are just as dimorphic). Currently, it seems that the genus originated in Asia with A. hezhengensis, before quickly spreading into Europe and Africa, and even reaching North America by around 7.5 mya, with the southernmost occurence there being in Guanajuato, Mexico with A. alvarezi. They replaced the dwindling bear-dogs and hyainailourids as the apex predators across the Holarctic and Africa. At their size, species of Amphimachairodus could likely have taken on even the biggest herbivores of their time like giraffids, chalicotheres, rhinos and even proboscideans.
Competition included the agriotheriin bears, which were similarly widely distributed across the Holarctic, while other machairodonts (like metailurins and basal smilodontins) likely steered clear of these giants, other than Nimravides, which also reached immense sizes around the time Amphimachairodus entered North America (with Nimravides lahayishupup). Albanosmilus and Barbourofelis, the last nimravids, were also potential competitors, though still smaller and they vanished by 7 mya. Upon entering North America, A. coloradensis would have also encountered the borophagine dogs, including the giant Epicyon haydeni (if only for a short while, like with Barbourofelis), which is also around the time the modern canine dogs first radiated into the Old World. A common competitor for the Eurasian Amphimachairodus would have been Dinocrocuta, a lion-sized hyena and the biggest of its family, though Amphimachairodus would ultimately outlast it as well. At Chad, the gigantic A. kabir coexisted with fellow scimitar cat Lokotunjailurus and potentially early versions of Dinofelis (a metailurin) and Megantereon (a smilodontin), dwarfing all of them, and it also could have preyed on the hominine ape Sahelanthropus, often touted as the oldest representative of the lineage leading to humans. Its fossil record ends around the Miocene-Pliocene boundary, but the lineage didn't go extinct, but rather gave rise to Homotherium, which reached similar global success during the Pliocene-Early Pleistocene.