That's the basketball court up there! It does exist and there are many stories about why it was built. One story claims that Anaheim had a law that said only gymnasiums could be built as tall as the Matterhorn needed to be. Walt Disney placed the basketball hoop inside the mountain so that city planners would have no choice but to allow the mountain to be built. An interesting story, but it falls apart quickly. Why would a gymnasium ever need to be that tall? Could DISNEYLAND possibly believe that the city of Anaheim would classify a mountain as a gymnasium just because it had a basketball hoop in it?
So why was the hoop placed in the Matterhorn? Nobody seems to remember the exact reason, but it was most likely put there to be used by the mountain climbers who scaled the peak daily during the summer months. They needed something to do in between their "climbs".