HMs exist informally in PMD 2, in the sense there are specially-coloured discs that teach Cut, Surf, etc. But they aren't required to access certain dungeons like they are in PMD 1, and most don't interact with terrain.
Some areas of some dungeons can only be traversed by certain Pokemon, e.g. only Water-type and Flying-type Pokemon can go on water tiles. A complete guide is available here. There are also some moves (including Rock Smash) that can be used to destroy walls in dungeons. There are also areas of the final dungeons that can only be accessed with a key, even if you can walk through walls.