My advice would be don't bite off so much at once where you'll risk getting discouraged. Part of the reason you may be feeling overwhelmed is that it sounds like you're combining three projects: learning a new programming language, learning network programming, and writing an application server in a new (to you) domain. Any one of them is potentially enough to keep you quite busy.

Why not instead start with a language you already know, and figure out how you'd sketch out a standalone game engine (forget about networking for now) in that. Then once you think you've got the basic game engine (architecture, at least) down, then tackle turning it into a network server (again, still using a language you already know.) Finally, port the thing over to a language you want to learn (Elixir/Scala/whatever) and you'll have an implementation you understand well to compare it against. Of course you can rearrange the sequence... but that's the basic idea.