Chiefs may have only had 182 yards, but the big plays in the games were passing plays. Those last 2 touchdowns were brilliant using the Eagles defensive tendancies against them.
Also, the reason, the Chiefs could run some is because they were the #1 passing team in the NFL this year. When you pass and use the entire field, you have so much more space to do anything you want, whether that be running inside, outside, passing in any zone.
Best team in the NFL is the #1 passing team. I believe the last teams that won because of a dominant running teams were like 2-3 decades ago. The early 1990 Cowboys and the late 1990's Broncos.