Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the rice is tender and liquid has been absorbed, 20 to 25 minutes.
Combine rice, coconut milk, sugar, and salt in a pot; cook and stir until thickened and creamy, about 20 minutes.
Beat milk and egg together in a bowl. Spoon 1 to 2 tablespoons rice mixture into milk mixture and beat to warm and temper milk mixture. Slowly pour milk mixture into rice mixture while constantly beating; cook, stirring constantly, until pudding is heated through, 2 to 3 minutes.
Remove pot from heat and stir coconut oil, vanilla extract, and coconut extract into pudding; refrigerate until chilled, about 1 hour. Garnish pudding with pineapple wedge.