From what i'm aware both demo and final version on Itch.io are to be downloaded then extracted on local drive and played via launching the exe file (or apk install on phone). I was unable to get the zip to work straight from the Itch io app, maybe if they made some updates from the last time i tested. Also, there might be a way to register the game into the itch io app after it's installed (unzipped), i recommend checking the itch io support forum (https://itch.io/board/24575/butler)
DLsite version (demo and final) : can only be downloaded then unzipped and played.
I hope this helps