Yes, you're talking about a device behind NAT which initiates a connection to an external service. However, we're talking about a service listening behind NAT

Yes, you're talking about a device behind NAT which initiates a connection to an external service. However, we're talking about a service listening behind NAT (in this case Call of Duty on an Xbox at home) that needs to be listening for connections initiated by other Xboxes to establish a P2P connection. This is what port forwarding enables and this is what uPnP automates.