When the XOR Gate has only 2 inputs, it is a "one and only one" gate. However, when the XOR Gate has more than 2 inputs, it is no longer a "one and only one" Gate... It is no longer about exclusivity, it is about detecting an odd number of TRUE inputs.
This project "The Exclusive Gate" is about a circuit that has more than 2 Inputs (4 in this example) and only outputs TRUE if "one and only one" input is true.
