Certainly at first glance "The Keeper of Cademuir" does not look like a typical horror story. As the OP summarised, a gamekeeper finds a poacher's trap, gets his hand caught in it while he investigates its mechanism, and spends hours in a state of despair until he is finally released when the poacher returns.
Like many of Buchan's protagonists, the keeper is physically strong and vigorous, a "man of a bold carriage, with the indescribable air of one whose life is connected with sport and rough moors". So it seems very exaggerated how rapidly he is reduced to despair. He first panics, and then rages, after which he sleeps for an hour, dreaming that “he seemed to be dead and in torment... a thousand evil spirits were mocking his anguish”. He then hallucinates, “all the wholesome sights of a summer day were wrought by his frenzied brain into terrible phantoms”, and imagines how he will die, and his wife will forget him and remarry. Before he falls into unconsciousness, he weeps "unnatural tears, which, if any one had been there to see him, would have been far more terrible than his frantic ravings.”
Why would a physically strong man be reduced to this condition over the course of an afternoon? Having a hand trapped in a snare is painful and annoying, but the descent into delirium is extremely rapid - the keeper is almost dead by the time the poacher returns. In her thesis on The fiction of John Buchan, Kate MacDonald argues that
an intimation of evil is strongly present in the atmosphere
and that that is the cause of the keeper's "unnatural terror". This is certainly supported by the keeper's feeling of evil spirits mocking him, and that the tears he shed are stated to be "unnatural". A formless evil, driving the keeper insane, would certainly be grounds to classify the story as a subtle example of the supernatural genre.