ONCHAN, Isle of Man—It takes an hour by plane and almost three by ferry to reach this island-country smack in the middle of the Irish Sea. Here, on top of a bluff with magnificent views, is a modern building shaped like a Victorian-era hotel that was once on the site.

It is the headquarters for PokerStars, the largest online poker company in the world by a wide margin. And it is from this unusual perch the company is playing a difficult hand: just two years after being shut down in the U.S., and with its founder living here...