nat – How does the website "whatsmyrouterip.com" detect the IP address of the LAN router and the IP address of the LAN device as well as the IP address of the WAN gateway router?

The website http://whatsmyrouterip.com/ can be used to resolve the public Internet WAN IP address of a gateway router. However, it also displays the private IP address of the gateway router and the private network address of the device sending the request (for example, a laptop).

How does the site access IP addresses of private networks, knowing that the NAT source IP address of the page request is that of the gateway router? HTML headers?

FOR EXAMPLE. Public IP address of the gateway router: 257.59.201.1. Private LAN address of the 192.168.1.1 gateway router. Private LAN address of the laptop 192.168.1.25.

The site is HTTP, so all this information is submitted in clear text.