If we include the entire animal kingdom, there’s LOTS of things that don’t swim. Even some aquatic animals, like sponges, or the bottom-dwelling clams, for instance.
As for vertebrates, they all evolved from fish and would have to have lost the ability at some point to qualify. On a planet as watery as this, that seems like it would be real survival disadvantage; even deserts flood occassionally.
What candidates do we have? If memory serves the only uncontested vertebrate entry is the giraffe. Frankly, I’m skeptical. They may not be great swimmers, but they have big lungs and, one would expect a large center of buoyancy well below their nostrils. They might not propel themselves in the water terribly well, but I would think they’d float with their heads above water and be able to move along as well as, say, a horse. Until I drown one myself, I’m inclined to withhold judgement on the giraffe as a non-swimmer.
I think what we’re looking for is a creature with a body plan in which it either (1) cannot float (2) cannot, while floating, keep its mouth or nostrils above water, or (3) has no limbs that can move it through the water. These are the things that seem to constitute “swimming” to me.
For (1), vertebrates have either lungs or gills, and I’m unaware of any vertebrates with gills who can’t swim. So if an animal has lungs, it should generally float unless it’s tissues are extremely dense (although I, personally, will sink to the bottom of a ten foot pool unless I keep my lungs fully inflated). I can think of two ways tissue density could become very dense - shells, like with turtles, and absorbent materials like fur or feathers that could become water-logged. Turtles can swim, and I’m unaware of any animal that can become so water-logged it can’t float (that may just be my personal ignorance, though, they don’t really focus on this stuff in biology class. If there is a non-swimming vertebrate, this may very well be the reason).
Wrt (2), an animal may float but be unable to float in an orientation that lets it breathe. I don’t know of any such case, but it’s possible. Any land dweller where the center of gravity was closer to the mouth than the center of buoyancy would be a candidate.
As for (3), it’s highly unlikely. Literally any limb that moves ought to be able to provide at least SOME propulsion, and even the limbless snakes can swim quite well.
So there’s a few characteristics to think about, but I know of no vertebrate that exhibits them so strongly they can’t swim.