I had a look at that field but it was a bit odd. In the walkmesh viewer there's four green lines (denoting Location groups) but there's only three Location groups that are visible in the editor; the two for the ladder and one for the slide (that's unused but probably functioning). The one that handles the door seems to be missing, but functions in-game. Maybe it's because this area was done during the demo phases so there's bits and pieces the editor doesn't recognise? I scoured the other groups for script that handles the door but couldn't find anything.
What you should try first is maybe enabling the Jessie group's 'Contact' (it's set to disabled in her Init). But if that doesn't work, then best guess as to the actual issue is that the game is tracking Cloud's current triangle ID on the walkmesh and continually updating a variable with it. In the 'dir' group's Main script it tracks the Cloud group's Triangle ID to [6][0]. I'm gonna guess that when this variable falls within a certain value, it triggers certain events to happen (a fragment of the old Biggs scene and the unused slide above are there, the triangle IDs for them being stored in [6][2] and [6][4]; at least, the values here correspond to the triangles where these would be triggered).
The reason the Jessie group might not trigger it is because the game is only tracking the Cloud group's position. If changing Jessie's Contact to enabled doesn't work then you could maybe add these lines to the 'dir' group's Main, underneath the line tracking Cloud's Triangle ID:
-) 'Wait 1 Frame'
-) 'Store Triangle ID of the group 'av_j' in [6][0]
-) 'Wait 1 Frame'
If you're lucky, this'll make the Jessie group open the door when she reaches it, as the game will likely just check [6][0] against whatever it is that triggers the door. I don't know if the frame waits are necessary, but best to be safe. Only thing is, if the door is handled by a location group then the [6][0] check might not be used anymore; the other things, like the slide, don't seem to use it now either.