How does a common theme in the novel involve isolation of the gifted child?

The theme of isolation is definitely explored in this book. Regarding "the gifted child," the world that Card has created has two exceptionally gifted and isolated children. Ender is the isolated and gifted child in the Ender's Game series, and Bean is the focus of isolation for the Ender's Shadow series.
Right from the very beginning of Ender's Game, readers are introduced to an odd concept. Parents are only allowed to have two children, yet Ender is a "third." His family was granted special permission to have a third child, so Ender is isolated in that way. Other "third siblings" don't exist in his world, and the other kids aren't afraid to let him know it. That kind of isolation is almost inevitable, but much of Ender's isolation is intentionally done to him by the adults in charge of the Battle School. Their thinking is that Ender needs to be isolated so that he can be free to think of his own solutions instead of learning and following the status quo. They say,

“Isolate him enough that he remains creative—otherwise he’ll adopt the system here and we’ll lose him. At the same time, we need to make sure he keeps a strong ability to lead.”

One specific way in which they do this is by giving Ender the Dragon Army. Nobody wants to be a part of this army, because it gained a reputation of losing every battle. Graff resurrects the army and puts Ender in charge of it. The soldiers are mostly inexperienced soldiers, and Ender quickly goes to work at changing "toon" sizes and tactics in order to turn Dragon Army into a very capable group.