Yemeni President Abed Rabbo Mansour Hadi fled the country by sea Wednesday on a boat from Aden, as Shiite rebels and their allies advanced on the southern port city where he had taken refuge, captured his defense minister and seized the city’s airport. Hadi’s departure marks a dramatic turn in Yemen’s turmoil and means a decisive collapse of what was left of his rule, which the United States and Gulf allies had hoped could stabilize the chronically chaotic nation and fight al-Qaida’s branch here after the 2011 ouster of longtime autocrat Ali Abdullah Saleh. Over the past year, the Shiite...