Horses and dogs do walk, trot and what's called canter or gallop (in horses). The trot is a two beat diagonal gait. It can be any speed or level of enthusiasm as long as the diagonal front and rear leg move in unison. If they don't it is another kind of gait. A horse can even trot on the spot.
Obviously humans with only two legs only have one cadence for waking and running. But we borrow the word "trot" from animals for a human doing some kind of slow jog, not exactly a run.
In horses and humans and dogs, a trot can be any degree of speed and liveliness. A horse can certainly have a slow lumbering trot, especially a horse that is big, heavy, older, or footsore. And so can a human.
He's not swift and athletic in his movements. He might be overweight or just not built with a runner's body type. He's trotting (faster than a walk, slower than a run) but he doesn't look graceful and he's using a lot of energy to do it.