That sounds like a pretty radical change in Catholic teaching. It sounds like Francis is saying belief isn't necessary for salvation—all you need is to do good. The headline is perfectly crafted to play on arguments between Catholics and (some) Protestants about the role of faith and works in salvation. "See! I told you the Catholic Church thinks good works can save you!"
Indeed, for me, a Christian Universalist, the headline made me wonder momentarily if I need to hie me into the arms of the Mother Church.
Fortunately you don't even need to go find Francis's original speech to discover how misleading the headline is. You just need to read the parts of his speech which were quoted in the article itself.
"The Lord created us in His image and likeness, and we are the image of the Lord, and He does good and all of us have this commandment at heart: do good and do not do evil. All of us. 'But, Father, this is not Catholic! He cannot do good.' Yes, he can... The Lord has redeemed all of us, all of us, with the Blood of Christ: all of us, not just Catholics. Everyone! 'Father, the atheists?' Even the atheists. Everyone!" (Pope Francis)
In that quotation, the relationship between redemption and doing good is explicated in just a few sentences, as a hypothetical dialogue between the pope and a catholic follower:
Catholic Follower: But Father, this is not Catholic! He [a non-catholic] cannot
Pope Francis: Yes he can… The Lord has redeemed all of us… not just Catholics.
Catholic Follower: Father, the atheists? Even the atheists?"
Pope Francis: Everyone!
Take a look at Pope Francis's first line in that dialogue. He denies a claim that non-catholics can't do good, and gives his reason for this denial—namely, the fact that "The Lord has redeemed all of us." In other words, everyone can do good because everyone is redeemed. Again, in other words, according to what Pope Francis said, redemption enables good acts. This is in keeping with Catholic theology, which holds that part of what Christ accomplished by dying on the cross was to free all human beings, past and future, from bondage to sin. In other words, because everyone is redeemed, no one has to be evil.
But the headline implies exactly the opposite. It implies Francis said that doing good deeds leads to redemption. But that wasn't what he said at all. He said that redemption leads to doing good.
There has been a fairly large backlash against Francis in some Protestant circles (read comments to any of these articles) because people are either reading only the headline, or allowing the headline to poison their understanding of Francis's speech. (The article itself hardly helps, quoting portions of the speech then completely misconstruing them immediately afterward. But a blog post isn't the place for a detailed analysis of every error!) And many of those responding positively to the speech are doing so based on the very same misunderstanding!
This is an example of why it is so super important for everyone (those who write headlines and those who read them in particular!) to be in the habit of reading carefully and critically, and withholding judgment when they haven't had a chance to do so.
It's important also to note, by the way, that in catholic theology, redemption is not the same thing as salvation. A great many commenters (again see comments to the articles found in the previous link) are coming away from this article believing Francis has claimed that everyone is or will be saved. But that is not at all what he is saying. The problem is that different Christian denominations have different understandings of the term "redemption." In some denominations, redemption is the same as (or tantamount to) salvation. So when this article mentions redemption, many non-catholic Christians read their own concept of redemption into it and end up completely misunderstanding. Part of careful, critical reading is to be aware of the possibility of such misconstruals. When someone says something that seems surprising, one of the first questions we should ask is this: "Is that person using those words the same way I use them?" Getting an answer to this question first can solve a lot of problems before they even become problems.