Thankfully (IMO), you can't patent game ideas. There's no legal action NYT can take (and expect to win) to shut down any games that build on the same game rules.
However, even if you disagree with me, and think that there should be no app implementing Wordle-style gameplay on App Store. What's your opinion on Minesweeper, Tetris, or Tic-tac-toe? Should no iOS versions of those games exist? Remember that Apple only ever refers to the original Wordle website in their rejections and never even acknowledges the existence of Wordle clones.
What about Scrabble? If they were applying their rules consistently they would surely kick out Words With Friends, but what about Wordfeud? Should they kick out Wordfeud because Scrabble implementations already existed on the web?