Alien Geometries: Comes into play as the tests become more and more difficult, the higher they ascend the tower; the challenges begin to involve higher-dimensional shapes and arcane math.
Cloning Gambit: Part of The Reveal about Childe. The first expedition to discover the Spire? Didn't exist. Childe discovered the tower himself. All those mangled bodily remains outside the tower? Those are all Childe; he repeatedly cloned himself, backing up his memory each time. He died over and over again attempting to ascend the tower. Eventually, when he couldn't proceed any further, he decided to enlist the help of other people. So he made up the story about the first expedition as a cover.
Curiosity Killed the Cast: What's that? An ominous and inscrutable alien tower on a lifeless planet, you say? And you go inside and it tests you? And brutally punishes and/or kills you for failing? And the tests get harder as you go along? Sign me up!
Cyborg: Doctor Trintignant is absolutely obsessed with cyborg-ifying anyone he can get his hands on, including himself. Badly injured people (like those retreating from the Blood Spire after being "punished") are a great opportunity for him.
Cybernetics Eat Your Soul: Played with. Doctor Trintignant was already pretty immoral, even before he began experimenting on unwitting subjects (along with himself). On the other hand Richard and Childe become pretty warped in their quest to beat the tower; by allowing Trintignant to modify their bodies, they steadily become less human within and without.
Downer Ending: Everyone except Richard and Celestine are killed, with the possible exception of Childe, who might've suffered a Fate Worse than Death. Richard and Celestine are unable to reverse the radical changes they made to their bodies because society back home has collpased (thus the technology no longer exists) and Dr. Trintignant, the only other person who can do it, kills himself. They're forced to eke out a bleak and poor existence in Chasm City to survive, with Richard having to pretend to be a strange looking dog, due to his appearance. Eventually, the situation, combined with his memories and obsession with the Spire, causes him to give up and throw away his life with Celestine to return to the Spire (where he'll almost certainly be killed or worse, like Childe).
Dream Weaver: The night before their first attempt on the tower, Childe somehow feeds the plots of various "popular narratives from history" in an attempt to mentally prepare them for the challenge (see Shout-Out below)
Forbidden Fruit: Despite being unquestionably dangerous, the crew can't help but keep on going into the Blood Spire, even after people start getting mutilated and/or killed.
One character compares it to climbing a mountain: "Because it's there."
Genius Loci: Though never explicit, it's heavily implied that the Blood Spire isn't a simple structure but is in some sense alive.
Karmic Transformation: Possibly with Richard, the protagonist and narrator. He's repulsed by Doctor Trintignant's actions, but in his obsessive quest to beat the tower, he succumbs to more and more of Trintignant's modifications to make himself more able to complete the tests. By the end of the novella, him and Childe have had all their major body parts replaced and they resemble mechanical walking dogs covered in diamond armor, rather than humans.
Meaningful Name: A man with the name of Childe, in a quest to climb a Dark Tower? Who would do anything to beat the tower, including dying multiple times, in a loop, and sacrifice his friends?
Never Found the Body: Mostly averted, in that those killed by the Spire are unceremoniously ejected from the tower (sometimes in pieces, depending on how they died). Thus, the land surrounding the tower is littered with the remains of those who previously attempted the tower. Played with in that the Spire keeps any mechanical parts, and in the end, Childe's body is never found, implying either the Spire "harvested" him or that he had become entirely too mechanical for the Spire to eject.
Nothing Left to Do but Die: Doctor Trintignant's reason for committing suicide. He knows Richard and Celestine will ask him to undo the radical modifications he performed on them when they return. However, he considers it his greatest work, and he can't bear to undo his greatest work. So he kills himself rather than go through with it. That's right, he killed himself just to spite them.
Schmuck Bait: Near the end, its speculated that this might be the ultimate purpose of the tower. It lures in intelligent beings with it's tests, forcing them to adapt their minds and bodies to pass it's increasingly esoteric tests. Then when they finally get to the top they're "harvested" by the tower, like some kind of alien Venus Fly Trap.
"I had the same dream," I said, wonderingly. "And there was another dream in which I was inside some kind of-" I halted, waiting for the words to assemble in my head. "Some kind of underground tomb. I remember being chased down a corridor by an enormous stone ball which was going to roll over me."
Title Drop: "Diamond Dogs" refers to the monstrous forms Childe and Richard modify themselves into in order to beat the tower; by the end of the story, they resemble rottweilers standing on their hind legs, covered in a diamond fabric.