It’s not so dire because you can continue to play “classic” Wordle forever — or well 2028 at least. It’s a static, front-end only app with a predetermined word list iterating in order.
I'd imagine NYT could technically copyright strike anyone that hosts it, given that they've now bought the copyright to that particular arrangement of words. I wonder if it will come to that. This has an "Ethereum Classic" feel to it...