For a single-player game like this, instead of having it always running, I wonder if you could simply design the game in a way that the next state is deterministically calculated based on the time. So the next time you start the game, it loads the previous state + current datetime in order to produce the next state.

This would be prone to manipulation, if someone were to change their PC's datetime, but would give the illusion that it's always running without actually doing so.