Evan Spiegel has perfected the art of keeping people guessing about his true nature and ambitions. It’s a fitting accomplishment for the co-founder of Snapchat, who’s building his budding tech empire on the belief that modern communication should be brief, private and fleeting.

So far, advertisers and media partners have been willing to look beyond uncertainties about long-term plans, anxious as they are to reach Snapchat’s fast-growing audience that has moved well past 100 million daily active users.

But lately Mr. Spiegel’s ambitions for his company are coming into clearer focus. There are growing signs Snapchat is evolving into a media firm, one that given its appeal to young and diverse audiences could be a formidable competitor to both traditional media companies and other social media outlets.