It mirrors it in level design, overall mechanics, quest structure.
The main hub world mirrors what other zelda have done before like all the versions of Hyrule Field.
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The objectives in God of War are also similar, you're to trudge through a series of areas and bosses to reach the end point. The end point in this case is to just reach the top of the mountain to scatter ashes instead of rescuing someone. But that's just a surface level detail and it really could be anything. It's theming it doesn't have any real effect on how the game plays.
Throughout both God of War and Zelda, upgrades and items are strewn about the world in a similar fashion. You are to solve puzzles with items you've acquired throughout your journey to open up more places of the world to find these upgrades usually.
As far as the levels are laid out God of War still takes cues from other installments from Zelda.
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Skyward Sword had the areas leading up to the main dungeon be part of the dungeon in itself. While games like OOT, MM, Twilight Princess did not have this. It was mostly corridors with puzzles to solve along the way. That's what Skyward Sword used primarily, Skyloft was the overlworld that lead to these dungeon areas through beans of light. The on foot sections of skyward sword were often designed to be singular passages leading to an open area often with a puzzle or a series of enemies and then back to singular passage. Both games had you running through a gantlet to reach the end point.
God of War may not be based on a singular version of Zelda, but it certainly takes mechanics from a bunch of them.
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Combat in GOW took inspiration from the Souls series that part is true, but Zelda made it's own attempts at trying to make realistic sword combat with parries and blocks as well a few times. Again Skyward Sword tried with motion controls and prior you had Twilight Princess attempt to shoehorn that in. But Neither of them really hit the mark while GOW gave more depth to it's combat instead of just having it be mindless slashing like most other versions of Zelda had for normal encounters. It got right what other Zelda installments failed to do.