When he killed the man he was happy because he had finally killed the old man. This scene is important because it is the main plot in the story. In the text, it says " There entered three men, who introduced themselves, with perfect suavity, as officers of the police."
The cops are confronting the guy. This seen is important because they are finding out what happened and why there was a shriek. In the book, it says " I took my visitors all over the house." The guy started to turn pale so they knew something was wrong.
The guy is nervous about killing the guy. This is important because he is admitting to the cops that he killed the old man. In the text, it says " But the noise arose over all and continually increased." They went to the room and found out about the old man.