I'd be most interested in seeing what those percentages are in just the first halves of games - i.e., before most NFL games are so out of reach that teams are forced to abandon their normal game plan/scheme...

My hypothesis: Teams that are the most successful at running the ball, are the teams that are the most successful when it comes to winning football games. Success running the ball is a proximate cause of these teams' success, and that success running is what is causing the higher percentages of running that we see here. It's not just that they're way ahead, so they run more to kill the clock because the game is out of reach... it's that they GOT ahead by running more, and doing it better than those other teams.

I also hypothesize that another contributing factor is that most defenses are SOOOOO built to stop the pass - playing 5 DB as base, DL's built more on pass rush instead of run defense, etc., and the teams that recognize this and retool their offenses to be more run-heavy are the ones that are going to be more successful - at least for a while, until the defenses re-adjust...