Yahtzee Croshaw said:
You have a big angry bloke who seriously needs to get over something, generally a lady friend.
Gabriel Belmont was not particularly angry in the game. I would say more that he was conflicted, and not just for personal reasons, and if you watch the end (before the credits...), he makes peace with everything he's done and forgives himself.
They take it out on non-human creatures with a weapon that incorporates a chain so that it can have a decent reach.
Kratos kills humans too, incidentally. He pretty much kills everyone. Gabriel only kills the monstrous. And every single action game I can think of has that. Even TFU has you killing Rancors.
It has quick light attacks and slow heavy attacks,
Well.... technically Castlevania divides it into single enemy and multiple enemy attacks. Both do have light and heavy attacks, but so does just about every game ever.
as well as combos involving the two, air combos and the ability to grab and instakill the enemy with the circle button if you're just completely bored with tossing the guy around.
Every action game I can think of has air combos. Castlevania does have some grab insta-kills against some enemies, and not *every* action game does. Though a lot do.
You gather souls from enemies and use them to upgrade your combos and magic spells you learn along the way, and collect things that eventually make your health and magic bars bigger.
Just about every single action game has this. (I can't think of an exception off the top of my head, but there are a couple I'm not completely sure of... like I can't remember if you upgrade your health bar in NG2, but you certainly collect 'souls')
Then at the end of it you kill whoever the local equivalent of Satan is.
Hades is God of War's equivalent of Satan. So even God of War doesn't fit this formula. Unless you just generically mean "The game has an end boss". And all action games do.
Many games mix and match some or most of these elements but the three that do every single one of them are God of War, Dante's Inferno and Castlevania: Lords of Shadow.
Apart from not *technically* being true, due to Gabriel being a different sort of protagonist, why exactly do you think this is? Might it be because you cherry picked? Bayonetta and Castlevania share a timed block/dodge slowdown mechanic that none of the other games have. God of War shares multiple selectable primary weapons with Ninja Gaiden II, and Castlevania does not have this. Ninja Gaiden II and Heavenly Sword both have chain weapons.
Almost everything you listed is *extremely* common in action games to the point that nearly every one has it. The only exceptions are chain weapons and grab finishers. These aren't the feature for feature copies you want to make them out to be.