DUBAI—Around the time Mohamed Alabbarlaunched his $1 billion e-commerce firm Noon, the Dubai billionaire gave his employees a piece of advice: If you want to go home at 5 p.m. each day, don’t work for me.

“I want people who sleep in the office,” says Mr. Alabbar, the founder of the now three-month-old startup. “Want to go walk your dog in the afternoon and all that? I’m not the guy you work for.”

A...