The IP you're seeing (220.127.116.11) is the address your router is exposing to the outside world. The router is masking you're real address to keep you safe.
Any device that uses that router to connect to the outside world will be 'seen' as having that same IP. This is why your Mac and your iPhone appear to have the identical IP's when viewed from outside your network. The public IP is the address of that router (I'm trying to keep this simple because networking can get really complicated fast).
Your router is responsible for taking the individual device traffic and routing them to the correct device within your "private" network.
To use BlockheadsServer correctly with your Mac, it's best if you contact their support to determine the best way to configure it. You don't want to misconfigure a router because you might accidentally open-up your network to malicious activity.