Suits, along with everybody else who thinks about the meaning of words, works in the shadow of Ludwig Wittgenstein, who famously addressed the question we're discussing in his Philosophical Investigations:
Consider for example the proceedings that we call "games." I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? Don't say: "There must be something common, or they would not be called 'games' "—but look and see whether there is anything common to all.
Wittgenstein rejects the idea that there exists a finite list of criteria like Suits' that precisely delineates games from non-games. He continues:
How should we explain to someone what a game is? I imagine that we should describe games to him, and we might add: "This and similar things are called games." And do we know any more about it ourselves?
Wittgenstein is skeptical that the set of "games" can be exactly circumscribed at all. At best, one gives examples and draws out "family resemblances"—activity X looks a bit like checkers and a bit like whist, and there's something in it that recalls hacky sack, so we call it a game.
That doesn't mean there are no right answers. It is a fact that basketball is a sport, and it is a fact that sautéing zucchini isn't. And I think it's a fact that the math Olympiad isn't a sport either. Sports have goals—to score touchdowns, to pin the opponent, to strike a distant target. On the surface, a math contest has the same nature—you're supposed to solve a set of problems within a certain time span. But that doesn't reflect my experience. Working on a math problem is a solitary, contemplative act. That's true whether you're in a room full of precocious teens in Athens or at home in bed before getting up for breakfast; whether the problem is the Riemann hypothesis or something you solve in nine hours at the Olympiad. You're alone staring at the guts of the confusing, inexplicable, irritating universe, and the problem you're working on seems like a small part of an impossible-to-finish job. If it's like anything physical, it's like mountain climbing—only what mountain climbing would be like if the whole world were a 45-degree upslope, with no peak and no opportunity for final triumph. That's not a sport. It's something better: a game you can't ever really win.
Special thanks to Graham McFee, author of Sport, Rules, and Values, for helpful philosophical advice.