Does API gateways such as Zuul or Ngnix require backend services to be exposed externally as well?
Normally, you would not expose your backend services externally. The gateway (or the ingress) serves as the external gateway and proxies the requests to the internal network.
I am familiar with one use case where I expose some services directly: I do not want to expose some admin services running on my cluster to the external world, but I want to expose them to my VPN, so I have an ingress forwarding traffic between the external network and the cluster, and nodePort services that expose admin apps to my VPN.