If you want to enable this alternative view, you need to click on the new "Times Extra" button at the top of the front page of NYTimes; you can always click on "Switch back" if you don't like it. Regardless, users will automatically be switched back to the regular view after 24 hours. Therefore, you can't really start using this feature regularly even if you want to, except if you're okay with switching back to it once per day.
Nevertheless, it's an interesting experiment for NYTimes. It's akin to something Sphere and Blogrovr have been trying to do for a while, but I've never seen any of these as crucial; a slightly useful addition to your regular browsing habits, perhaps. News aggregator Techmeme, however, is essential to me, but it's also the very best at deciding which conversations are really relevant; we'll see how well NYTimes' algorithm will do with this regard.
The look itself is confusing: there's simply too much going on there. Techmeme works so well because of its simple structure: you can quickly skim through the "main" stories and delve into individual articles only after you find something interesting. NYTimes adds boxes with additional sources quite erratically, and I expect many users to get a headache, reverting to the standard view very fast. It would be a pity, though, if this initiative were to fail because of unfortunate design choices; I like the fact that the NYTimes is looking forward and finally not shying away from giving some of its traffic away, as I believe lots of linking is the best way to do news on the Internet.