A Netflix for video games? Why a longtime dream is closer than ever to coming true.

When Cory Burdette awoke recently to learn that Winter Storm Gia had caused a two-hour school delay in Reston, Va., he seized the chance to do a little family bonding. Plopping down in front of the TV, Burdette and his 5-year-old daughter spent the morning together playing Minecraft, the Lego-like adventure game where players construct buildings out of virtual blocks. "We play all our games together on the Xbox," he said. "In Minecraft, we both get to build a house together, find monsters and explore." The first time he fired up the game, Burdette had to wait for Minecraft to download and install on his Xbox before launching it.