This is a general post about why static classes cause you more trouble than they are worth. And this includes singleton classes which are just a fancy way of doing the same thing that avoids construction order problems. No advice fits all cases, so take it as advice, not as an instruction that it is always better to do it this way.
In general code shouldn't reach out to get the data that it needs to provide it's job, it should be provided with that data.
I'll give an example from what you said -
**Accessing settings options (such as screen size and keyboard bindings) would be easier accessed**
So you write you main rendering loop and in there you call something like
That all works well and is nice and easy. Then one day you decide "wouldn't it be nice to let the player make screenshots. And it would be good to do them at higher resolution than the screen so they look good!". Now you have a problem. All your code depends on getting the screen size from the static getSetting function. If instead you'd provided your rendering code with the screen size instead you could simply call it with different parameters.
Another problem -
You write an amazingly cool user interface class for your game. It needs to know what font the user has chosen so you call Game::getSetting(UIFont) to get it. Nice and easy. But then you decide to write a separate game editor... Now in order to use your amazingly cool UI class there is a dependency on your static Game class so you need to drag in the whole of the Game class too... Which probably has dependencies on other components.
Sure you can change the code to work differently, but then you have two copies to maintain. If only you'd provided the font as a parameter to the class instead of letting it go get it itsself it would be much easier.
In general having functions go out and get the data they need to do their job introduces coupling between components and makes your code harder to maintain and change, and reuse, and you are better providing from outside the data that is needed either as a function call parameter or when you construct an object or whenever.
And the main advantage of static data or singletons is that they are easily located in random bits of code. If you don't need random bits of code to reach out to the static data then it doesn't need to be static any more...
Note that this doesn't mean you need to pass dozens of separate bits of data. You might create a group of related settings where you generally need all of them for related purposes and pass that. For example make a UserInterfaceSettingsContext structure and store the related settings needed to draw a user interface in there and pass an instance of that to anything that needs it...