This "paradox" doesn't work!
If all the hotel rooms are full, you can not simply move a guest to another room.
In the paradox, does it imply that EVERY guest is changing room at the same time or one by one.
If the new guest moves into room 1 while guest 1 is moving into room 2, etc, there will always be 1 guest on the move indefinitely.
So to accommodate every new guest, the same amount of guest would have to be on the move and technically without a room while moving.
If it implies that ALL the guest is moving at the same time, this is not possible because there is no vacant room to move to since EVERY room is occupied already.
So, either you can accommodate a new guest by forcing a guest on the move or you can not accommodate any new guests because ALL the rooms are already occupied.