What are examples of horror in the story aside from the niter and the constant references to the dark and damp tunnels they walk through?

Certainly, the fact that Montresor is so good at hiding how diabolical he is and how he ruthlessly plots to deprive another person of their life represents an example of horror. He says,

It must be understood that neither by word nor deed had I given Fortunato cause to doubt my good will. I continued, as was my in to smile in his face, and he did not perceive that my to smile now was at the thought of his immolation.

He essentially smiles in his enemy's face while he quietly plots that enemy's slow and cruel death. The thought that another human being could be capable of such wickedness, even when "insult[ed]," is pretty terrifying.
Poe's use of dramatic irony—when the reader knows more than a character does—is also terrifying. Montresor says immediately that he intends to kill Fortunato, but the reader has to wait a very long time to see Fortunato not only realize this but also to see the action taken. This builds suspense. As Montresor leads his prey further and further into his "white web-work" of niter (this description itself horrifically symbolic of Montresor's predatory skill), getting Fortunato more and more intoxicated, we can only wait and see what horrible thing the protagonist is planning. We know Fortunato's fate, but he does not, and this produces the story's horror as well.
Likewise, the use of verbal irony adds to this effect. For example, Montresor calls Fortunato his "dear friend"—obviously untrue and seemingly spoken sarcastically. Further, when Fortunato's cough compels Montresor to insist that they leave the catacombs, Fortunato says that he "shall not die of a cough," and Montresor knowingly replies with, "True—true." He knows that the cough is not what will kill Fortunato; instead, he will do it himself.

In the literary genre of horror, authors create a sense of dread and fear in the audience, which gives the reader an unsettling feeling of angst, excitement, and terror. Poe's classic short story "The Cask of Amontillado" creates horror by revealing an in-depth look inside the mind of a murderer, who plots and carries out a perfect crime in order to get revenge on the unsuspecting Fortunato. Poe incorporates various elements of Gothic literature and the horror genre by illustrating a vivid depiction of Montresor's psyche as he plots Fortunato's murder. Montresor's calculated plot and his facade of civility are unsettling and remind the reader that dangerous individuals can easily disguise their malicious feelings. Along with the murderous plot and Montresor's terrifying capacity for dissembling, Fortunato's imminent death and his vulnerability are also horrific. The fact that Montresor buries Fortunato alive and gets away with murder is also particularly terrifying. Overall, Poe's ability to provide a vivid depiction of a murderer's psyche and incorporate various elements of Gothic literature make "The Cask of Amontillado" a particularly unsettling, horrifying story.