Ender's Game incorporates a lot of themes. It's hard to pin down just one theme that it's focusing on. Whether it was Card's intention or not, the book appeals immensely to "smart" kids who've been ostracized and isolated for their perceived difference from others in terms of intellectual ability.
Understanding Ender's state of mind in this case provides some insight into how real kids like this feel. Ender really isn't happy about being the forced into the role of being better than everyone else. He didn't ask for it. He knows what it entails and he ultimately doesn't want to do it. This is how the kids this book appeals to feel. They feel their intelligence is often not a blessing, but a curse, and there have been many instances where they would gladly trade it for the social acceptance that their peers seem to enjoy. At other times, though, they revel in being a cut above the rest, even if it leaves them lonely and outcast.
Secondly, it offers a systematic breakdown of social ostracization that occurs between children. If you haven't been the victim of it first hand, you probably wouldn't realize this, but the pattern of the ostracization that Ender undergoes is nearly identical to how it happens in schoolyards across America. There's very little variation. The oppressors have it down to a science. It happened to me, repeatedly, and the methods and techniques used by my torturers were the very same used by Stilson, Bernard, and Bonzo against Ender: the ringleader, the weak-willed cohorts, and the systematic ridicule and belittling of the target. Card has some knowledge of how this pattern works, and he is succinct and direct about portraying it. He does not oversympathize with Ender. Ender responds to it as best he can. He ultimately holds his own against it, which I think is the only unrealistic part about it. Usually kids are powerless against this sort of attack, and even the best and brightest tend to be the hardest hit. Ender's defenses are admirable, though his execution of them is perhaps a little optimistic on Card's part. When the targets are forced into contact with their attackers daily, there's simply no effective defense when they're as outnumbered as Ender is.
Finally, the last major theme Card plays on is societal expectations of brilliant children. Ender has a greater mental aptitude than everyone around him, but he doesn't really rejoice in this. In fact, he rejects it (in his return to Greensboro after his stint at Battle School). His higher than average aptitude leads his adult guardians and teachers (so to speak) to expect more of him than they do of most children, and he ultimately must tax himself beyond the limits of endurance to deliver. He is extremely adverse to playing the IF's game, but he goes through with it because he is pushed so hard by the IF and because he sees himself as realistically having no choice in the matter. They force him to play a game that he must win or lose. Ender doesn't see the point of the game, and all he really wants is just to stop playing. This particular theme resonates especially at the end of the story, when the IF gets the bright idea to use this for their purposes, channeling Ender's desire for the games to end into the utter perdition of the Formic homeworld. Just as he ended the games with Stilson, Bernand, and Bonzo, now he ends humanity's game with the Buggers.
My edition of Ender's Game begins with an introduction by Card including a letter written by a younger teenager who was part of a gifted and talented literature program which focused around Ender's Game. He claims the book rang true for him and for the other kids in the class in a way few books ever have. Card's introduction maintains that he knew all along that kids who read the book would empathize intimately with it, while adults might not get it and might even be put off by it - especially if they weren't willing to face up to the fact that their pre-conceived notions about the puissance of gifted children might be horribly wrong.
I believe the secret to Ender's Game's success was just that it spoke very plainly, maturely, and unapologetically to the fears, desires, and problems of exceptionally brilliant children. There are enough of these children who read the book and saw it as sort of a Catcher in the Rye for their niche that it became the cult classic it is today. Remember, it was published in 1985 - just in time for the first kids who read it to just now be coming of age, and not without the memory of a book that was so important to them and to their notions of childhood.