The tweet isn't 100 percent accurate. While the 2015 Patriots did win a playoff game with under 40 rushing yards they didn't win the Super Bowl. I also checked to see if they meant the 2016 Patriots who did win the Super Bowl, but that team had over 40 rushing yards in all their playoff games that season. So two of the three teams who have won that way in the playoffs have won the Super Bowl.
But as to your question, I would just assume that he realizes that passing is a more effective and efficient way to win in today's NFL and it is entirely possible that his experience with New England influenced him. And playing to your strengths has always been a Belichick philosophy as well, so I would assume that's part of it.