There is no international law against abandoning ship or stipulating that the captain has to be the last to leave the ship, but the cruise ship was sailing under the Italian flag - it was registered in Italy - so Italian maritime law applies, and Italian maritime code criminalizes the act of abandoning ship.
Edited to add: Crew members have testified that the captain wasn't wearing his glasses at the time, and was having trouble seeing the control panel. Things do not look good for him.
Not directly, but in International waters, the Captain must comply with the International Safety Management Code, which has a stated purpose of ensuring the safety of the crew/passengers.
Ironically, one such case worth reading is the sinking of another Italian owned and captained cruise ship, the SS Andrea Doria