While I'm not aware of any titles that I would refer to as "clones", the question isn't far-fetched:
Multiple games have since cited Breath of the Wild as an influence. These include Genshin Impact, Ghost of Tsushima, Immortals Fenyx Rising, Halo Infinite, Elden Ring, Pokémon Legends: Arceus, and Horizon Forbidden West.
I would say the defining characteristic that sets Breath of the Wild apart from its contemporaries is its "chemistry engine", as they call it. That meticulously programmed system of interactions where absolutely everything in the world affects everything else in ways that are intuitive. Wooden objects burn, lightning strikes metal things, fire will melt ice, electrified objects will conduct through metal and water, etc. That, in tandem with its cel-shaded artstyle, minimalist piano flourish soundtrack, and general lonely, somber vibe in a mechanically lush but socially empty world. That's the identity of BotW.
I haven't played Genshin Impact so I don't know how deep the similarities are. It sure superficially resembles BotW if you squint and look at it from a distance. Big open world, vibrant cel-shaded graphics, live in-overworld combat, you can climb walls and soar with glider physics, they got the high fantasy plus inexplicably advanced magitech thing going on... definitely some marks on the bingo card, but not really things particularly unique to BotW, either. I have no idea how much Genshin Impact actually resembles BotW up close.
I would say the defining characteristic that sets Breath of the Wild apart from its contemporaries is its "chemistry engine", as they call it.
It's traversal. The interactions were cool, but mostly about the puzzles.
What BOTW changed was how exploration works. You see a landmark in the distance, start moving towards it, and figure out how to get there. There's nothing you see that isn't part of the traversal system. There are no invisible walls. Some things are absurdly high to climb, some things are slippery, etc, but everything you struggle to traverse is clearly a product of the systems the game uses and makes sense.
(The problem was none of that exploration got you anywhere interesting, but the core element of "everything you see is a destination" is the thing about BOTW that was groundbreaking.)
Genshin has a 7 elements system that partially does what you describe: Wood (or anything made of or affected by dendro) burns when exposed to fire (pyro), fire melts ice (cryo) and vaporizes water (hydro), water conducts (well, causes a damage reaction with) electricity (electro), etc. The outliers are stone (geo) which makes forcefield shields with some of the other elements, and air (anemo) which swirls up and spreads and reacts together some of the other elements.
Breath of the Wild took a somewhat novel approach to open-world in that it filled the game world with lots of interesting landmarks, then gave you lots of movement options and just let you explore on your own.
In particular, because Nintendo took a risk and introduced this novel concept into an established series, it had a big audience and enough budget to really show off that this concept works.
That's why lots of gamedevs took inspiration and steered their open-world games into similar directions.