Let’s get the obvious answer out of the way: this book is called “Ender’s Game” because it’s primarily about a kid called Ender, who happens to spend most of his time playing games. So Ender + games = “Ender’s Game.”
But wait, not so fast there – why is it called “Game” and not “Games”? Ender plays lots of games: he plays video games in the games room, and he plays laser tag in the battleroom, and he plays the simulation war games at Command School. And while we’re at it, why is it called “Ender’s Game” and not “Ender’s War”? After all, almost all of his games are war games.
We’re not 100% sure, but how about this: you wouldn’t want to call this “Ender’s War” because that would give away the plot of the book – that all of his games are really about war (or really are war). If you named it “Ender’s Games,” then the reader might think about Ender playing all the little games that he plays. But what’s important is that all the little games he plays all are really parts of one big game. A game called…life.
Just kidding, this game is called “Blow up the alien homeworld and hate yourself for killing off an entire species; but you never knew it was really war, you thought you were just playing a game; and maybe you’ve learned your lesson that war isn’t really a game, after all – or maybe all games are really versions of war?”
One last thought: “Ender’s Game” sounds a little bit like “endgame.” Besides being a play by Samuel Beckett (1957) and an album by Megadeth (2009, insert heavy metal guitar riff here), “endgame” is a chess term referring to, well, the end part of the game, when the players probably don't have a lot of pieces left. When you don’t have a lot of pieces left, you have far fewer options and it’s a lot easier for one small mistake to snowball into a catastrophe. To connect it to the book, we could say that Ender’s Game is like a chess endgame because there aren’t a lot of options left – it’s kill or be killed. (Or at least that’s what the characters think it is.)