Preheat oven to 325 degrees F (165 degrees C). Lightly grease a 9-inch springform pan.
Combine the coconut, gingersnap cookies, and melted butter in a bowl; mix until evenly moistened. Press the cookie mixture into the bottom and slightly up the sides of the prepared pan.
Bake the crust in the preheated oven until browned and set, about 10 minutes. Set aside to cool.
Reduce oven heat to 300 degrees F (150 degrees C).
Beat the softened cream cheese in mixer bowl until smooth. With beater set to medium-low, slowly pour the condensed milk into the bowl, mixing only until just blended, stopping to scrape the sides of the bowl as necessary. Add the eggs, individually, allowing the first to blend into the mixture before adding the second; again, scrape the sides of the bowl as necessary.
Pour about half of the cream cheese batter into a separate bowl. Stir the lime juice and lime zest into the portion in the new bowl; pour the batter over the crust in the springform pan, smoothing into an even layer.
Stir the coconut extract through the remaining cream cheese batter; pour over the lime-flavored batter in the springfom pan, smoothing into an even layer.
Bake in the preheated oven until the top of the cheesecake springs back when gently pressed, about 45 minutes. Turn oven heat off, but leave cheesecake inside with oven door slightly ajar until the oven cools completely. Refrigerate until completely chilled.
Prepare mango coulis by pureeing the mango with sugar until smooth. If too thick, add a teaspoon of water at a time, using just enough to make pourable. Drizzle over cheesecake when plated.