Camp owners are betting that the store’s combination of play space, toys, clothes and ice cream will not only make a profit, but grow the company into a national chain.

But experiential retail is, thus far, unproven. “I think the jury’s still out on how well they’re going to do,” said Richard Gottlieb, chief executive of Global Toy Experts, a consulting firm. “When you devote that much space to nonselling space, your challenges are greater in terms of turning a profit.”

Indeed, although the Ewing twins had spent hours playing at Camp over three visits, their parents had yet to buy anything.

But all of Camp’s stores seem to be located near young affluent parents. The original store sits just west of Union Square, and the company’s recent New York additions are in the high-end malls of City Point, in Brooklyn, and Hudson Yards on the West Side of Manhattan, both of which were built to anchor vast new residential developments. The Connecticut and Dallas stores are also in upscale shopping centers.

“F.A.O. Schwarz had a big load in rent, so they had to sell a lot of merchandise at a really nice profit,” Mr. Gottlieb said. City Point and Hudson Yards present the same high-overhead challenge, which is heightened by the cost of constructing their lavish play environments.

The company does have a plan to ease some of the pressure to sell. Mr. Kaufman was recently the head of marketing at Buzzfeed, famous for its product placements. Drawing on his digital media experience, Camp is bringing brand sponsorships to the store, charging companies to weave their messages into the play space. A cooking program, for instance, had a promotional tie-in with Bounty paper towels this year.

Regardless, Camp will need to move a lot of people through its stores. During the Ewings’ weekday visits to the Brooklyn store, which opened on Nov. 30, crowds were light. On a Friday, the twins shared the space with a handful of other families who stayed quite a while. On a Tuesday, they had the store nearly to themselves.

After rotating through dozens of activities, Krishna and Balarama battled their father in a Teenage Mutant Ninja Turtles video game, resisting when their parents suggested they move on. From the sidelines, Mrs. Ewing said, “We could spend all day here.”