I was thinking exactly this except the in and out doors would be on opposite sides (why would one door be in the floor?)
Surely it's because, as the "ring" is rotating, the centrifugal force pushes everything to the outside of the ring (that becomes the floor), and if the horizontal elevator / train moves around the outside of the ring, which seems to make most sense, then you would presumably leave the elevator / train through the roof and enter the ring through the floor (of course, when you enter the elevator it has no up / down, until it picks up speed and matches the speed of the ring).