Google's position is that they will index whatever content is at your site, so that users can easily search for it. If you don't want your content indexed, their crawlers honor the robots.txt standard. All you have to do is create that file and tell Google to say out, if that's what you really want, and Google will no longer index your content. That means, of course, that users searching for information with Google will no longer find anything from your site.
It seems even the clueless news organizations know that removing their sites from search engines is not a good idea; otherwise they would have already taken this trivial step. Instead, they continue to badger Google for money. In that context, this new offer from Microsoft is just what they have been asking for all along. It certainly solves the problem of how to monetize their existing content; they don't need to do any thinking or lift a finger (other than blocking Google's crawler), and Microsoft will pay them.
The big question is whether this strategy can succeed. If News Corp cuts itself out of Google's results in return for their own little slice of Bing cashback from Microsoft, the immediate result will be that the vast majority of search engine users won't see their sites anymore. Microsoft is no doubt hoping that if they can bring a few major content providers onboard in return for exclusivity payments, that will draw more web users to Bing. I'm not sure that will work.
If Microsoft succeeds, it would be a huge change in the way content is found on the Internet. Today, you can usually choose any major search engine and be relatively confident that you'll be seeing all that every major site has to offer. Sure, there may be some differences in the order of results across search engines, but most of it is there. In this future search-engine-bribe-driven world, you'll only be seeing a part of the picture. Search engines will no longer represent impartial seekers of content, but will return results driven by the business partnerships and payments they've received.