The origins of the Furude family in Higurashi no Naku Koro ni stem from a marriage between a human and a demon ( Hanyuu). Note: Hanyuu was older than the form seen in the 7th and 8th novels during said marriage.
Hatoful Boyfriend is a Dating Sim, like many others, where your character tries to romance cute guys. Only this time, replace "cute guys" with "photo-realistic pigeons".
To help players identify with the characters, there is an option for the intro scene of each love interest to show an image what he would look like as a human (answer: Bishounen). However, it is made clear that the birds really are birds, and this is just a visual Translation Convention.
Dra Koi is a love story between a nameless protagonist and a dragon who similarly has no name. She picked him out as the one who would slay her, a choice he can reject.