Colin Kroll, a college dropout turned startup millionaire, drifted through his company’s holiday party at Gran Morsi, a cozy Italian restaurant in downtown Manhattan. Dressed in a gray sweater and jeans, he chatted up employees and their plus ones.

When one of his engineers offered to get Mr. Kroll a drink, he flashed a big smile. “I’ve stopped drinking. I’m trying to be healthier.” He’d started running regularly, too.

“Look...