Process shortbread cookies in a food processor until finely ground. Add butter; pulse 3 or 4 times or until blended. Press firmly into bottom of a 9-inch springform pan.
Beat cream cheese and sugar at medium speed with an electric mixer until smooth. Add eggs, 1 at a time, beating just until blended after each addition. Stir in piña colada mix and coconut extract. Pour into prepared crust.
Bake at 350° for 30 minutes. Turn oven off. Let cheesecake stand in oven, with door closed, 1 hour. Remove from oven, and run a knife around edge of pan, and release sides. Cool completely on a wire rack. Cover and chill at least 8 hours. Sprinkle pineapple evenly over cheesecake. Spread Rum-Spiked Whipped Cream over pineapple; sprinkle with coconut. Store in refrigerator.