The Alley Demons are recurring characters from the original game.
They act as hazards during the stealth segment in the Dark Alley and in the central room of The Sewers. Moving in front of their eyes will "kill" Madotsuki and set her back to the start of the segment.
In the Dark Alley, it is possible to jump over them using the Umbrella Effect. In either world they can be killed using the Mask of Fear, which is required to get past them in the Sewers.