First of all, keep in mind what dystopian means. In literature, a dystopian society is the opposite of a utopian (perfect or ideal) society. And, it is more than just a science fictional place. It is a society that is undesirable and typically moving toward destruction, or already there. Dystopias often contain environmental destruction and are characterized by governmental control.
Keeping that in mind, there is one predominant element that makes Ender's Game venture into the dystopian genre. The eminent threat of the Bugger's destroying Earth (and the first Bugger war) allows the government to control the world by fear. The two-child rule is one example of this. The "monitors" installed in every child are another.
Further, the Battle School, and the acute governmental control and manipulation that goes into training these child soldiers is another very dystopian element. It becomes more obvious as Ender progresses through the school and realizes (along with Dink) that the other armies are not the enemy, the teachers are.
While Ender is in Battle School, his sister and brother back on Earth are controlling a political war through "the nets" as Locke and Demosthenes. The fear of being caught by the government but the desire to lead a revolution anyway further reveals the dystopian side of society.