Yes, you can call it REST, in reality it also serves the static files (Elm's JS and some others).
I've used Elm because I find it the best thing that has ever happened to the world of front-end development, and because I now have quite substantial experience working with it commercially. Happy to tell more, but I think that would be an off-topic on this website.
Let me just say one more thing, I have most of my experience working with Haskell and Elm, and they can be combined together greatly, and I suspect the same story is possible for Rust. I'm looking forward in using Serde types to generate Elm encoders/decoders. That would make sure my APIs don't break and avoid unnecessary boilerplate.
Edit: forgot to mention, I'm using Redis and Amazon S3 at the moment, will probably add PostgreSQL for reading later.