I didn't look close enough in the developer tools to see the limited extent. From what I can see, just the email list sign-up forms on www.nytimes.com are using React, but all of the new front page of mobile.nytimes.com is in React. They are testing the new version of the mobile site in a partial roll-out, so if you open a new browser session there's a good chance the new one will get served to you (It will have a message saying "You’re seeing a test of a new version of the New York Times home page.").