We don't generally send SQL over the wire, though. :-)
That is to say, front-end programmers usually work with a middleware (or backend-as-a-service) layer that translates REST/JS API requests into backend storage, and PgREST simply implements this layer with Postgres itself.
EDIT: I did some research: there is no difference. It's just plain ol' rails-style REST. This project is basically taking your thin sinatra/express/flask API layer and pushing it into the database itself, for reasons I am as yet unable to ascertain.
The main difference is that back-end models, validation rules, triggers and views are coded in DB level via stored procedures written in Node.js-compatible modules, so it's enforced for both SQL- and HTTP-speaking clients.
As you pointed out, this is simply an instant JSON-over-REST API server on top of existing Pg databases, and is not intended to replace the need for traditional frameworks with server-side templating.
EDIT: how easy do you think it would be to do the authentication etc outside, at the level of the nginx proxy?
For authorization (authz) it's IMHO a bit better to handle it in the DB level, similar with Firebase's ACL lists.