I think there may be a bug in the example map where it's not showing the ID for that tile, the mystery "tile01" should be the tile in front of the door (the path end tile right outside the house), or "tile04" in the case of your duplicated script. The door itself doesn't change to a different tile, it just has an "opening" animation, and then using the Modify Navigation scripts along with the IDs takes care of changing the navigation paths so you can walk through the doorway once it is open (and prevents the character from clipping through the open door by preventing movement from "tile02" to "tile03").
In regards to the differences between the original and duplicated script, I recently added named constants for the navigation mode values so it defaults to using them now instead of the corresponding integer values. For example, WALK_AND_INTERACT = 0, WALK_ONLY = 1, INTERACT_ONLY = 2, etc. Either can be used, but I added the named constants so you don't have to remember the integer values when typing quick scripts. Here is the changelog that mentions the change: https://itch.io/t/73895/release-notes-for-v0410-alpha