Well, it is basically Hitchcock's reply to Dostoevsky using a fictionalized Leopold-and-Loeb-type scenario where the strangled victim is in a chest while they host a party with the victim's family with the chest containing the dead body in the very room.
From your article on Leopold and Loeb:
"In my course on the nature of evil, I teach the students about Leopold and Loeb, alongside Nietzsche’s works and the Alfred Hitchcock film
Rope which was loosely based on the pair. In
Rope, a teacher (played by Jimmy Stewart) espouses Nietzschean philosophy at first but is horrified once he realizes how his murderous pupils have chosen to act upon it. The obvious-but-grim joke is that I make students read Nietzsche while we watch a movie in which a teacher regrets making students read Nietzsche."
The whole movie is worth a watch philosophically, but the two key scenes that connect with Nietschze and Dostoevsky here would be this portion of the dinner party:
and the final scene where Jimmy Stewart's teacher named Rupert (who had been piecing together Brandon's excitement and the victim David's absence for what was really going on) figures it out and returns after the party to carefully confront the two:
I have to read
Crime and Punishment, but I wonder if Hitchcock may have downplayed the link to God comparatively? Seems so by what you wrote.