Here is a smart projector designed for Xbox gaming. The ViewSonic X2-4K has a 120-inch screen for movies and games. It has a 4.2ms response time and 240Hz refresh rate for ultra-smooth gaming. It has 0.69-0.83 short throw ratio, 1.2x optical zoom, vertical/horizontal keystone correction, and 3840x2160p resolution.
This projector has HDMI, USB-C, and USB-A ports in the back. It also has built-in Harman Kardon Bluetooth speakers. The X2-4K projector can be controlled using your Xbox controller.