Cagdas Halicilar, a former electrician-turned-Bezos-impersonator from Germany, stood on a dock near the Aman, waving at the passing boats. He hoped to deliver an expensive bottle of whiskey as a wedding gift, but was unable to breach the security bubble.

“It’s a dream to meet him and shake his hand,” Mr. Halicilar said. “I do this as a hobby — it’s not about money. It’s not even about attention. It just happens, totally automatically.”