So the folks at Distilled wrote a piece "Google to Announce that Links are no Longer a Major Ranking Factor," which is meant to catch attention but is not true. More of a "what if" story.
@realSEyOda mmm, no.— Gary Illyes (@methode) March 12, 2016
The bigger issue is that it seems SEOs don't get RankBrain. Truth is, how can you blame them, Google doesn't fully understand RankBrain.
But truth is, RankBrain doesn't replace ranking signals, from what I understand. RankBrain uses the signals, and more, to better tailor the rankings. So RankBrain uses links, as one of it's signals, to try to optimize the rankings based on better understanding the search query.
I don't think RankBrain can replace links, because RankBrain may use links.
Forum discussion at Twitter.