Passing efficiency most certainly correlates to winning more than running efficiency. In general, running is lower risk lower reward and passing is moderately higher risk and higher reward.
However, I think baked into this though is the fact that the easiest way to lose a game is the inability to stop the run. You may not see this in the NFL as much but certainly in college (more so back in the day) and high school. If a team is overmatched and can't stop the run, it is a quick route to a big defeat. Teams need to stop the run in order to make the passing game an issue. So, again "baked" into this is the fact that NFL teams commit significant resources to stopping the run, because if they didn't, it would be the quickest route to losing. There is no reason to believe for instance, that passing yards are inherently better, but it is just that yards per attempt is more likely higher than yards per carry at the NFL level. There is a little more risk, but generally speaking there is a great deal of more reward.
For instance, team A plays Team B. Team A defeats Team B with the following stats
Team A
20 rushes for 200 yards.
4 of 5 passing for 30 yards
Team B
20 rushes for 20 yards
4 of 5 passing for 20 yards
No one would say that team A won because it passed more efficiently, right. It won because it's offensive efficiency, particularly its running game was more efficient and productive, most likely. These stats are very unusual for the NFL, of course, because the teams are overall very even in athleticism and talent and generally speaking the running differential will not be significant enough to make a difference so the running game is essentially a stalemate and the passing game is the difference.