The keywords are route, routing and routers. That's what "internet gateway" does, they route your network traffic to other networks using know or configured routes.
NMAP is a great command line network utility for various purposes. But AFAIK, it cannot tell you which hosts are served as routers.
But even if you do find the other gateways/routers. They might not allow to route the traffic coming from your host to other networks (like Internet) depend on how they are configured and consider VLAN is often used these days.