N.B. As drawn, the circuit doesn't have any provision for damping the current in the relay coil at the moment the switch opens. This is OK because, apart from the LED current, there should be no current through the coils at the moment the switch is operated. However, if in the throes of your gaming passion, you are prone to frobulate the switches, it would be well worth adding anti-parallel diodes to both coils to clamp the back EMF.