Why is this a zero sum game?
A zero-sum game is one in which the players' payoffs sum to zero in every possible outcome of the game.
The given payoff description is incomplete. But if we assume that in the outcomes where only one player guesses correctly, the other player (who guesses wrong) would have to lose an amount equal to the total number of fingers shown (denoted $X$, say, to use @Bayesian's notation), then the game is indeed zero-sum:

In outcomes where both guess correctly or incorrectly, they each get $0$, which sum to zero.
In outcomes where only one guesses correctly, the correct guesser gets $X$ and the incorrect guesser gets $-X$, which also sum to zero.