Technically how do curl, ping and other tools get around an NGINX front facing reverse proxy server?

nginx is a web server, that answers to incoming HTTP / HTTPS requests. Whenever the interface that nginx is listening to can be connected from the public internet, nginx can serve web pages for it.

The access from other servers to internet is dictated by the network setup. In this case, all those servers have default routes to internet, so that their IP packets are forwarded to any public internet address by the edge router in the network.

These two cases are not related.

If there is a firewall on the edge of the network, then you can restrict the access of each internal server.