IN AN UNMARKED BUILDING on a quiet side street just off the beach in Venice, California, 26-year-old Snapchat CEO Evan Spiegel stands in a small conference room. He’s draped a towel over a mysterious object sitting on a table. He is eager to the point of jitters.

“You wanna see it?” he asks, grinning widely. There’s drama in this reveal: I’m about to join an exceedingly small circle of people whom Spiegel has shown the object to. As he lifts the towel, he breaks into a delighted laugh. “Boom!”

What...