The defense might have won the game, but it also kept the game closer than it should've been. The Dolphins won the turnover battle 4 to 1, its QB rating was well above Cincinnati's, and it had a sufficient number of rushes and yards per carry not to be one-dimensional on offense. These are all factors very strongly correlated with winning in the NFL.
With those differences in the game, the Dolphins should've won the game in a relative blowout, but what kept the game so close was the defense's inability to stop 3rd down conversions, and the ridiculous number of plays that gave Cincinnati. They simply had a tremendous number of chances to drive the ball down the field and put points on the board, which is exactly what made it a close game despite the differences I outlined above.