Basically, we used the Godot's rpc system to implement the multiplayer. Multiple server instances are running on our server and waiting for match requests. A matchmaker that we made with Rust is also running on our server and waits for clients. If enough clients have connected, it tells a server instance to start a match.
Once a match has started, each client sends updates to the server instance. The server instance then computes the new game state and sends relevant updates to the clients.
So, you could say it's a classical centralized client-server structure implemented using Godot's rpc system.
Unfortunately, there are no plans for open sourcing Erasterra as we have moved away from Godot towards our own engine.
We're currently working on a blog where we'll regulary give insights to the development of our "Sphere Engine" :)