As a Genshin player who has never played BOTW, I'll disagree.
What do they have in common? A bright fantasy setting with a large, more or less seamless territory to explore. That's not super-novel; it's sort of what we'd expect to see as table stakes on a fantasy game once we got computers big enough to maintain a large and busy world model.
I tend to think of Zelda games in terms of puzzles and item accumulation-- a major feature is always "when you get the item from Dungeon A, it unlocks the ability to finish that dungeon, and usually grants access to some previously unreachable part of the map to proceed to Dungeon B." By comparison, Genshin's puzzles are pretty anemic and highly optional.
I think their success is 33% an excellent UI (you have great flexibility in build and playstyle, but it doesn't require a bunch of complex gestures and keybinds) and 33% in providing a pretty environment to explore, and 33% Waifu Wars.
> What do they have in common? A bright fantasy setting with a large, more or less seamless territory to explore.
They have a lot more in common than that. Not to say that Genshin Impact isn't doing it's own thing, but there's clear inspiration in a lot of the mechanics. https://www.youtube.com/watch?v=TgLtAF7F_H8
