The story's main conflict, unlike many short stories, is not internal--it is man versus man in the sense that Kugler has struggled against mankind his entire human life and now must depend on men (humans) to deliver his eternal sentence. One could also argue that the story represents a conflict between the author, Kapek, and tradition. Instead of God being the all-knowing, objective judge, He is the witness. Kapek's reasoning for this--that God cannot be unbiased because He sees and knows all is certainly thought-provoking, but it does go against literary and religious conventions.
The story's structure is quite common except for the missing denouement. At the story's end, Kugler is sentenced to eternal damnation; there is no repentance, no opportunity for an appeal, and no lecturing from the human judges--the case is closed, and the judges call for the next case.
The story's exposition informs the reader where Kugler is and how he got there. The rising action includes the revealing of God as the witness, Kugler's life of crime and earthly death, and dialogue between God and Kugler. The climax occurs when the judges return to the courtroom and sentence Kugler to eternal death. This event serves as the climax because the story's rising action and conflict are resolved with the handing down of Kugler's sentence. The only falling action is the story's last sentence in which the next case is called.
You also asked about suspense. While Kapek does not rely heavily upon suspense, he does use it in the sense that as God discusses all of Kugler's actions, the reader thinks that perhaps there might be one bit of good in Kugler or a sense of repentance, but there is none. The climax, therefore, is not all that surprising or suspenseful.