If you were my boss at an animal design firm and I submitted you this proposal sketch for a climbing animal, you'd probably think about firing me. There's nothing in the structure of this animal that suggests it would be good at scaling things.
Those are Alpine Ibex goats scaling a dam in Italy to lick the salt off of the rocks. Question is, how the hell do those guys get up there and stay up there? Why isn't the bottom of the dam covered in shattered goat carcasses?
The answer lies in the design of the goat hoof.
Unlike horses, goats have hooves comprised of two split toes. The outer part of each toe, which is shaped like a parabola when seen from below and is labeled "Wall" in the diagram below, is hard; the part marked "Sole" on the diagram is soft and rubbery.
The parabolic shape of the hoof wall adds strength, while the cushy sole provides traction on sloped surfaces and can deform inwards to absorb irregularities in the terrain. And because the toes can operate independently, the goat can use just one to gain purchase on extremely narrow surfaces, or splay the toes to gain more contact area.
The image below is of goat poop. It admittedly contributes nothing to the discussion but I am including it for scatological purposes.