MARAWI CITY, Philippines—Bantog Panomblayan firmly stomps on broken red tiles abandoned on the ground. “Eto na ngayon ang bahay ko,” he says. “Na-mimiss ko nga ‘to. Nu’ng nakita ko, parang sumama loob ko.” (This is my house now. When I saw these tiles, I felt angry. I miss my home.) The house is gone. Only...