The fact that there logically exists a list of game entities, and that all threads are required to have a consistent view of these entities at any point in time

The fact that there logically exists a list of game entities, and that all threads are required to have a consistent view of these entities at any point in time and are allowed to mutate them, is a global mutable state. So for games - like for most non-trivial applications - some global mutable state is unavoidable. The task IMHO is not to eliminate it but to reduce it or at least restrict its "degree of globality". For example - even when you can't avoid global mutable state shared by threads within one client process, probably you can reduce the global mutable state shared by different client machines in a multiplayer match.