Other languages don’t have the concurrency primitives (spawn, send, receive), process linking and monitoring that OTP is based on.
At the core a process is an infinitely recursing function where the updated state is supplied on each recursive call - which is equivalent to an infinite iteration.
One uses Erlang/Elixir to take advantage of these features and to be able to structure behaviour in a way that isn’t possible in other environments.
Would you find this code easy to port another language?
Fundamentally you should chose Elixir/Erlang because it makes it easier to express the solution to your problem - it follows that it would be more difficult to do in another language.
In his book Seven Languages in Seven Weeks , Bruce Tate suggests that “Erlang makes hard things easy and easy things hard.”
Maybe the problem is that you are trying to classify “Game” as an entity rather than as the “engine” of the application - this reminds me of the thought concerns vs. runtime concerns discussion with regards to To spawn, or not to spawn? which had an influence in the rewrite of the book.
Coupling 
Essentially the Game “entity” you are looking for is either the GenServer state or some significant part of it.
So indeed to allay your concerns you could factor that part out - away from the GenServer if you wish.
I presume we are talking about this:
https://media.pragprog.com/titles/lhelph/code/gen_server/lib/islands_engine/game.ex
