The Bad Sleep Well is not a Hamlet
Hamlet is not just "a guy gets revenge on his father's killer". That's not even the main thing! The emotional core of Hamlet is the drama between the prince and the other members of the court: these people he's known as his life, his own mother, are all backing Claudius, and only Hamlet (and Horatio at Hamlet's urging) believes him to be a murderer. It's the tension between those two understandings of the world, and in Hamlet's doubts of his own purpose, which are the core of it. If the Claudius equivalent isn't at least metaphorically marrying the protagonist's mother as well as ascending to the throne, it's not a Hamlet.
(The Lion King isn't a Hamlet either for the same reason. Scar does literally marry Simba's mother, but absolutely no one is chill with it.)
