Has Nintendo shut down a game because it cloned the gameplay of one of their games?
I'm developing a game that very closely mimics the gameplay of the ghost minigame from Nintendo Land. I'm not including Nintendo characters, names, etc.
Is there any precedent of Nintendo going after people for something like this?
Nah, you can't patent gameplay mechanics unless they are super specific and interconnected.
Taking what's good from other games and turning it into something new (or similar) is known as remixing and it happens all the time. Like mentioned in another comment, Palworld did this by taking the fun elements of different genres / vibes (Pokémon, Survival games, Shooters) and making that into a game.
Even the Pokémon Company had to put a statement out basically telling the Xitter drama seekers to shut up and stop reporting the game for infringement, because there wasn't any.
Just make sure (like you already mention) not to use assets, sounds, names and other IP related subjects.
It still grinds my gears that Warner Bros. patented the Nemesis System they used in their shadow of war/Mordor games. I'd love a whole genre of those kinds of games with different settings and themes.
Even in their case, the phrasing within their patent form is fairly specific to their games. Unless one completely clones the system, I would be surprised if they got legal trouble for it. Better to check with a qualified lawyer of course.
The games have a number of captains, and they will sometimes fight among themselves. The winner will get stronger and level up. The player can attack these captains, too, who may have a strong point or a weakness. If the player dies while fighting, the captain grows stronger and will taunt the player on a rematch. If the player manages to make the captain flee and live, he may develop a fear for the player
There are many things that can define the captains, such as fears (of the player, of fire, of wargs), weaknesses (to stealth, to arrows, to fire) and even immunities (to arrows, to stealth, you get the drill)
Also, if the player dies to an unamed orc, said orc will become a captain. I vaguely remember some captains coming back to life, if they weren't decapitated on the killing blow. They return weaker, but will comment on wanting revenge.
As a final note, Shadows of Mordor is a pretty fun game. Think of it as Assassin's Creed exploration with Batman Arkham City combat. Not the most faithful game to Tolkien's work, but it's good.