Yes, but not every land animal, some can outrun Homo on the long distances as well (wolves, horses, deer). Mammoth couldn't and died. Moose cannot as well, but survived somehow.
> Other animals, such as deer, bison and others, have bodies more suited to quick, short-distance running. The difference means that an average human being in running shape could catch a horse, deer or almost any other animal by pursuing it to exhaustion.
https://phys.org/news/2024-05-theory-humans-evolved-ability-...
Besides, ancient horses were much smaller and couldn't carry a rider, hence chariots. I would like to speculate that smaller means better thermoregulation, so smaller horses fared better on long distances versus Homo genus.