In this interesting history, which is the actual description of the origin of this use from Professor Corbato, he explains that daemon originally had the connotation of "an attendant ... or indwelling spirit" and that
By the late 16th century, the general supernatural meaning was being distinguished with the spelling daemon, while the evil meaning remained with demon.
He goes on to share the story of Maxwell's daemon. Maxwell was a 19th century scientist would posed a physics problem in which a tiny daemon was the attendant at a gate between two chambers that was large enough for a single molecule. The daemon observed the molecules and chose which ones to allow to pass through the gate.
So now we come to the crux of it. We have established a daemon as an attendant, and a scientist used a hypothetical daemon in a famous problem in which the daemon's job was to monitor molecular movement. Professor Corbato wraps up his explanation with
As you probably know, the "system processes" called daemons monitor other tasks and perform predetermined actions depending on their behavior. This is so reminiscent of Maxwell's daemon watching his molecules that we can only assume that whoever dubbed these "system processes" had Maxwell's daemon in mind.
The history also notes that Professor Saltzer, who also worked on Project MAC with Professor Corbato at the time "daemon" came into use for this purpose, confirms that this is the origin of daemon as it is used in computing.