Yes the picture's real. Burj Al Arab in Dubai is home to the world's highest tennis court (at times). At 210 meters (about 690 feet), it's pretty far up there. Way higher than I'd feel comfortable running around hitting a ball. The court doubles as a landing pad when there aren't any matches being played, and as a place to shit your pants the rest of the time.
Video of Andre Agassi and some other guy playing tennis up there after the jump. I like how at the end they just start wailing balls off of the side trying to hit things. Because that's what I would do.