Why does Amorous require admin privileges on Windows?

Just, why? It's just a game.

 

Are you running it through the launcher? Because if you are, that launcher installs files.

 

You're probably referring to the launcher, which writes lots of files to the system and depending where you place it on your system, may need special privileges to access it. There's also probably some other technical reason I'm not aware of that Lennian will provide.