Q - Does the game require two players?
A - Though the game is designed for two human players on two DS units, an AI practice opponent is also provided for a single player game.
The AI plays reasonably well, and is good enough to help you learn the basic strategies of the game. However, a decent human player will be able to beat the AI, even at the higher levels, quite easily. And besides, this is a game about second-guessing your opponent and trying to read their mind---emotions, tilting, and other factors come into play, and it's just not the same against an AI.
So, though playing against a friend is not required, it's certainly recommended, eventually.