I think you can create a Google account using a non-Gmail address. That's the way employer-based Google accounts work, for example. They may or may not using Google for handling email (eg could use Microsoft for email and Google for other stuff).
No doubt a bunch of stuff assumes it's going to be @gmail.com though.
Can't you delete the gmail account from the phone? If the Hotmail address is a Google account presumably that works for Play Store etc?
But calendar stuff may get added to the Google Calendar associated with the Hotmail address, rather than the MS calendar in Hotmail. Maybe the latter needs some kind of calendar sync thing (CalDAV?).
Theo