Hippopotamuses are heavy, dense creatures that are capable of running underwater. However, they are quite bulky and short-legged. Could an animal have long, slim legs, like a horse or deer, while still retaining the underwater running capabilities of a hippopotamus? Some problems might be that the legs would be far heavier than terrestrial creatures, and that it would pose a greater falling risk if it were forced onto land, but on the other hand, it would give the advantage of letting it run quickly while all other creatures must swim, which is almost always slower
Could they run underwater, if they are dense enough, yes
Will they be any faster than hippo, no.
the drag water produces means the length of the limbs becomes largely irrelevant to speed. you need a lot of muscle and leverage to push through water with any speed. Worse the limbs experience a lot of drag as well, so a long thin leg may actually end up moving slower.
You also have the problem of center of balance, your creature will not be able to do if the water is moving, its center of gravity is too high to stay on its feet if the water is moving ay any angle to their direction of travel. Hippo get away with it by being short and squat.
Did you know that orcas have a taste for moose?
I'll let you take some time to digest that morsel of information. And no, I am not making this up.
Now that I got your attention: moose can swim at 6 mph, which is about Michael Phelps's top speed underwater. The difference being that moose, despite never getting the gold in the Olympics, can sustain that speed for much longer. That's much faster than my own fat ass jogging on land, and they swim with a kinda walking motion, so I count that as running underwater and running pretty fast.
That's also 20% faster than hippos, who only do 5 mph in water.
Last but not least, moose are taller than horses, and arguably slender.
Crabs do ok running underwater.
This animal has long slim legs like a crab. Ghost crabs are lightning fast on land. This one is making pretty good time, moving along the bottom underwater. I am sure it is helped by the fact that it does not have density-lowering air filled spaces inside as we landlubbers are obliged to have.
I think a hydrodynamic shape would help in this endeavor and especially a shape that at speed would push you against the bottom to retain traction - like a spoiler on a drag racer.
If anyone can find better video of crabs moving fast along the bottom link them up. Especially if you can find one with a spoiler.
Horses can already do it if their heads stick out
The following video shows a horse walking along the bottom and then swimming even faster when the water gets deeper. It wouldn't take much in the way of evolution for horses to develop higher density and to learn to hold their breath.