This brand of lamp normally has both plugs facing "forward" like the one on the left. Most power adapters can't fit, because of the black square piece right there. Now, if it's loose -- and they frequently are -- you can twist it about 30° to one side and wedge your power adapter in there. But there's no way to twist it to face a full 90° like the one on the right.
Someone "fixed" it. I've been to this hotel dozens of times, and none of the other rooms have it like this. I guess it's just a matter of having a screwdriver with you ... but who took the time? Some sort of Robin Hood electrician is on the loose.