How does the hinge mechanism of plug-type pressure doors work?
This video has a clear shot of how a classic plug door (in this case of a B737) works (or search for flight attendant training videos).

You can see the door pops in (tipping a bit downwards) and then rotates on a axis in the center of the opening and then moves outside sideways. This is possible because of how the geometry works out, moving sideways negates the boor being wider than the opening and tipping down lets it fit height-wise.