Converting Kinect depth coordinates to work with Unity

We are very new to working with the Microsoft Kinect, and are trying to hook it up to our Unity 2D game for a class project. Part of our class project requires that we project the game onto a fabric, and have the user press the fabric in order to interact with the game. The player will tap the fabric in order to collect falling objects. We are trying to use the depth map with the Kinect in order to see where a user has tapped on the screen, and then we can see what object they are interacting with. We are having trouble finding a way to transform the Kinect depth coordinates to coordinates that work with our game. We are unable to use skeletal tracking due to our set up. Does anyone have any experience with transforming Kinect depth coordinate data to a 2D Unity game without using skeletal functions? Below is a diagram of our set up for clarification.