Since the OP was not very specific, here are two very different answers to the question depending on what he means.
OPTION A: How to fill the niche of Equus without a single-toed Equidae
The single toe design is not just about speed. Any mammal with a digitigrade foot has the same advantages, but in many ways the hoof is an inferior design to the digitigrade foot because it can not dig its digits in for extra traction, it does not spread out onto soft sand or mud for extra support, and it can't use its toes for gripping uneven terrain. The only real advantages of the hoof is that you minimize the number of structures to injure. That said, in open dry climates, the foot's flexibility becomes much less important allowing a single toe design to become an option.
The big reason you don't see single hooves on much bigger or smaller creatures is that larger ones like elephants need feet that spread out so they don't sink into the dirt, and smaller ones don't need the extra structure to not hurt themselves and benefit more from the flexibility of multi-toed feet.
While the single toe design is a solution in this specific environment, it is a narrow niche. In theory, you just need to disrupt the environment enough to push the horse out and let a more flexible multi toed ungulate take its place.
To push out or prevent the horse, you just need to do one of the following:
- Introduce an apex predator that can match the horse's speed, but lacks the agility to reliably catch its competitors.
- Major climate change. Too much rain and the horse loses traction in the mud, to little rain and it loses traction in the desert sand.
- Major food supply change. This will encourage all animals in the niche to become either bigger or smaller. The horse can not function as well at other sizes; so, it will be selected against in the evolutionary arms race for size change.
- Make another animal more favored by humans for the same niche in our civilizations. Human preferences have had a huge impact on what species survive and which ones go extinct. Horse hooves make great glue; if another animal made for better mounts, we might have easily hunted them to extinction by now like so many others who made the mistake of having useful body parts.
Once you eliminate Equus or one of the common ancestors required to get ot equis, a multi-toe ungulate could fill the same niche for a few million years until evolution forces the 1-toe design onto the multi-toed animal.
OPTION B: How another ungulate could evolve to become a single-toed horse like animal.
The most likely animal to fill this role would be an ungulate of horse-like size that already lives in the plains and similarly relies on speed as its primary mode of survival. One really good candidate for this is The Wildebeest. It is Bovidae not Equidae at all; so, it brings in a few new features to pick from including horns and stripes. The reason I lean towards this animal is that it is the fastest grasslands ungulate of horse like size that is not part of genus Equus. They have a top speed of ~50mph and weigh in at ~600lb. This is a bit smaller than most horses, but if the horse were to never exist, environmental pressure may encourage them to become a bit bigger to fill the same niche currently held by zebras. As they get bigger, their feet would come under the same set of evolutionary pressures that favored the single toe on horses, making their convergent evolution a distinct possibility.