In "The Guest" by Albert Camus, what details are omitted from the story as a whole? How might your response to the story be different if they were included?

That is a great question.
First, let us acknowledge that all fiction leaves things out, and short stories leave more things out. They have to, in order to create the focus authors need. So, leaving things out is not a weakness in a story. It’s essential.
Turning to this classic short story by Camus, a number of crucial details are left out. Some of these would reshape my response to the story considerably. Consider, for example, the accusation scrawled on the blackboard in the final paragraph. If we knew that the person wrote that was mentally ill, or had a feud with Daru, or simply didn’t represent the community, that would radically change the ending of the story.
A second key detail relates to Daru, where he’s teaching, and his internal states. Camus tells us Daru lives simply, like a monk. Why does he live so simply, and why did he take this teaching position? Camus presents us with the current reality of the story, but not the background, and that could change our emotional response to Daru (and his actions in the story). We’d feel differently about Daru with more background.
Finally, it would change many people’s reaction to the story if Camus gave more details about the crime for which the prisoner was being held. If we knew there was some sort of justification to the killing, it would be different than if it were an outright, cold-blooded murder. Our sympathies would change.