Firstly you might check to see that their usage agreement on the web site allows you to copy the information. By default, it's copyrighted, so unless they say "feel free to copy this", you can't. That might get you off the hook on having to do it
Secondly, if you do have permission, it's called "screen scraping", if you're googling it. Essentially you'd need to CURL the web page over, and parse through it looking for the news of interest. Not particularly fun stuff, and of course if they change the page, your site is likely to break.