I still get the log-in page. Do they only let you view the story once?
It works fine for me, even though I'm not signed in. However, I just saw a notice that, beginning next month, visitors will only be allowed 10 free articles rather than 20. I didn't know they were doing that. I have seen cases where a newspaper will let you view one or two articles, then make you sign in.
So, it's possible you've exceeded your free article quota, and I haven't. Try removing all your nytimes.com cookies. That will probably reset your quota.