This game was heavily influenced by the likes of the 3D zelda based games. Large dungeons with puzzles. Special item in dungeon to help you beat puzzles and the subsequent boss battle. Boss battles result in a new heart container. Heart container pieces are all over the place. There are lots of places like "I want to go there, but I don't have the hookshot yet." type of stuff in the large overworld. The dungeons aren't plentiful, but they're pretty hearty. Items/potions are kept in bottles, which much be purchased or earned. There's even a horse like Epona. They probably use the horse better than any zelda game has thus far too.
The only not quite zelda aspect is the combat. It's got the z-targeting mechanic, but there are combo attacks spread over 2-3 buttons. Sword/subweapon (scythe/gauntlet) or... souls are collected a la the god of war green/blue/yellow system. One type of soul is currency for new items/moves/etc. Different types of combos. Juggle moves... but it's nowhere as complex or serious as something like DMC or Bayonetta... there's probably 15-20 total listed combos/moves... but it's a lot more than a zelda game.
The oddest element is that you can pick up cars and rocks and whatever and beat demons/angels with them... not sure where that even comes in, because it reminds me more of a prototype/infamous sandbox game type element.