Gameplay is fun! I think in more difficult levels you could do with hiding the next few buttons you have to touch until you reach them. There's a lot of charming jokes in the names of the illnesses and the demons, but they don't really come through because most of the text is really small and the font doesn't help (also the green clashes a lot with the rest of color palette.. but at least it stands out). I also like the dissonance between the setting and the music. Overall the tone reminds me of Shin Megami Tensei games.
EDIT: Also I like the use of the theme + limitation. A doctor who's so evil that his hell is literally just having to do his job is really funny.