Yes, I have stayed in one of those. It's also referred to as a "turrett" balcony room. These are on the end of the "fingers" of the building, if you are standing at the Swan looking toward the Dolphin there are four "fingers" ...two off the east wing and two off the west wing. The rounded turrett part is the extra covered balcony, which enter through a door in your room. The regular balcony is the uncovered with a sliding glass door like the other balconies along the sides of the finger wings.
Other than the extra balcony it's pretty much a normal king room, maybe a little roomier and much brighter, with more spectacular views, due to a large window on the wall where the door to the balcony is (which you don't have in a normal balcony room along the hallway).
Great rooms for a honeymoon! I would think it would be lovely to have room service breakfast or dinner on the end balcony!
I don't know about the robes and have never done room service at the Dolphin ...but have fun!!
But have fun!