I like the occasional "idea" story and this was a pretty good one. Most of it's about the explanation of the concept, and talking about different details of it. And as long as those details are interesting enough it strings you along, as you wonder "Could these exist in our world?" "what would I do if I found out how to do this?". Yeah, it was relatively lacking in conflict, but I enjoyed it well enough.
That being said, I think it could've done with a bit more conflict. Sure, he's looking for a particular door for his friend to go through, but that's not really a conflict for our narrator. He wants to go through Doors, and going through Doors is how he finds new doors, so he accomplishes both. Even when he's trapped there's not really any conflict to speak of. He's been stuck in there for whole minutes, he calls the one number he finds on the wall (because we all know how well cell phones work when you're in a cave, right?). The woman tells him her terms (giving her his list) and those terms do not harm him in any way; he agrees and she lets him go. In addition, he gets exactly what he wants from her just by asking.
I didn't mind it ending before we see the friend cross through, because there wouldn't be much to see there. It just would've been nice if it had a bit of conflict to really make it complete. But I enjoyed it anyway.