"Checkers is my favorite game" is correct.
It is hard to explain it! In my mind, do different things are going on.
One is that you are equating two things: [Checkers] is [my favorite game]. They both need to agree in number. In both cases, we are talking about a game. We can't ever say "are my favorite game." From our real-world knowledge and from the structure of the sentence we know that "Checkers" is not really a plural here.
The reason why it isn't really a plural is that "Checkers" is really short for "the game of checkers." If we say something a little different, "The game of checkers is my favorite," I think you can see that in this sentence the subject is the word "game."
Finally, in my mind, "Checkers" is simply "a name that happens to end in "s." For example, President Nixon had a dog named Checkers. Obviously, you would say "Checkers is the President's dog," not "Checkers are the President's dog," because in this case we understand that we are shortening the sentence, "A dog named Checkers' is the President's dog."