Centaurs would an obvious one. Hellhounds and Werewolves would probably be able to outrun a horse due to pure stamina.
Most flying Mamono like Harpies, Wyverns and Griffons would be able to fly faster than a horse.(considering that Horses are actually food to Griffons)
And if you got a Wurm or Sandworm on your tail, even with a horse, good luck trying to outrun that as one simply smashes her way through any obsticle while the other can literally swim through the sand.
Allmost all I would say. Even human (doesnt need to be athlete, but needs to be quite good physical condition) can outrun a horse.
Let's not forget that humans were originally hunter gatherers, and horse, before dometication, was nothing more than food and tools, and humans did hunt them with only crude spears, clubs, and other crude tools as weapons.
Sure horse runs a way faster than human, but horse runs only couple hours. human runs longer distance than horse, but it will take servial hours.
How ever due domestication, selective breeding etc we now have horses that run further than their ancestors, and majority of humans arent much better off than what they were back when they were hunting horses, so it depends slightly on a time frame too.
The biggest difference that makes a rider faster than runner/walker is mostly the fact that the rider doesnt need to carry everything by himself.
For example I as fairly average human wouldnt have too much trouble walking 45-50km/day (30 miles give or take couple miles.) But add there backpack full of food, tent, water, some basic tools and/or weapons, and that would reduce my daily distance easily 10-15km/day leaving me to do 35km (21miles) at best. and most likely around 30km (18miles)
But give me a horse to ride on (brisk trot, and occasional gallop) horse doing the majority of the carrying I would only do around that 50km (bit over 30 miles) a day. Althuogh if I'm aiming to go long distance, I would most likely keep the horse in mind and do only 30-40km (20-25 miles) per day
How ever with horse I could mout likely outrun just about every monster that doesn't fly, Brake the line of sight, and after that it's all about can I cover my tracks / scent etc. from the mosnter that's chasing me.
Modern endurance riders that go for as far as possible in one day, can cover well in excess of 130km (80 miles) but that's with just horse and rider, and nothing more, supplies come with a truck or van. But again we must remember that these horses are bred and trained for these long distance runs.