Preheat the oven to 350 degrees F. Wrap aluminum foil around the bottom and halfway up the sides of a 9-inch springform pan to prevent any leaking.
Combine the cream cheese, agave, soy milk, pumpkin, tofu, arrowroot, agar, cinnamon, and nutmeg in a large mixing bowl and stir together. Transfer to a blender and blend until smooth and ingredients are fully integrated. This may have to be done in batches. Pour the mixture into the prepared springform pan.
Put the cheesecake in a large baking pan and fill the pan halfway with hot water. Bake for about 2 hours, until lightly browned. Remove, let cool, cover, and refrigerate. The cheesecake can be made up to 2 days ahead of time.
To make the cider reduction, combine the cider, sugar, and nutmeg in a pot and bring to a simmer over medium heat. Simmer, stirring occasionally, until the mixture is reduced by half and is syrupy, 1 to 1 1/2 hours. The reduction can be made and refrigerated up to 2 hours ahead of time. Bring to room temperature before serving.
To make the frosting, mix together the confectioners' sugar and buttery spread in a large bowl. Set aside. Combine the coconut meat and vanilla extract in a blender and blend for 2 minutes. Transfer to a stand mixer or to a bowl and use a hand mixer. Add the confectioners' sugar mixture and cream cheese and mix thoroughly until a smooth frosting is formed.
To serve, remove the foil from the pan. Run a knife around the outer edge of the cheesecake and release the springform pan clamp. Put the cake on a plate or cake stand. Pipe frosting on the pie as desired. Drizzle the reduction over the cheesecake. Cut into wedges and serve.