There was a doctor and two nurses on duty at the time. The doctor had to be quite resourceful: he checked my vitals, took, developed, and interpreted the x-ray, and then set the broken bone. I gather the doctor(s) onboard also wind up serving as the primary care physician for all of the staff on board, too.
The facilities themselves were quite sparse, and with somewhat dated but still functional equipment. The x-ray used film, after all. He also wound up using a spoon from the dining room as a splint, because the ship didn't seem to stock small splints.
My understanding is that shipboard medicine has advanced considerably since then. Some cursory Googling suggested that ships are routinely equipped with satellite connections to doctors on shore, ecgs, defibrillators, and the like.
In other cases passengers have been airlifted either to shore, or in one case a navy aircraft carrier, which is equipped to do surgery. That implies that reasonably advanced medical care is available ona ship, even if cruise ships are not setup to offer it. I'd link to the article, but I'm on a tablet and it's easy to find.
Although there are some ships doing cosmetic surgery at sea, and there are proposals for cruise ship medical tourism.
Also, I would not call that surgery.
I'd argue that Comfort and Mercy could do more good for US national security at sea, combined with LPD/LPH for cargo transport and personnel, than any other surface ships in the US fleet -- humanitarian missions probably improve security more than anything but the submarine nuclear deterrent.