DUBAI–As the West grapples with a historic downturn in brick-and-mortar retail, Dubai’s mega malls are mixing fun and shopping to weather their own challenges.

For years, Dubai has combined entertainment and shopping to support a healthy clip of economic growth. The city’s malls are now morphing into leisure destinations of their own, offering everything from aquariums and underwater zoos to flight simulators and indoor ski slopes. Prime space once reserved for department stores are going to gyms, spas and clinics, say analysts, as malls seek to insulate retailers from the challenges posed by more people shopping online.

“The idea is to bring more and more people into the malls,” said Matthew Green, head of research and consulting for CBRE in the United Arab Emirates. “Footfalls usually convert into sales.”

Evidence so far suggests the entertainment-driven retail strategy is working.

The operator of Dubai Mall–one of the biggest malls in the world–said it received more than 65 million visitors at its properties in the emirate in the first half of 2017, an increase of 7% over the same period last year. Mall of the Emirates, another of Dubai’s giant malls, welcomes more than 42 million visitors annually, according to its owner, Majid Al Futtaim, one of the largest mall operating companies in the Middle East.

Most Dubai malls don’t disclose the value of retail sales, but in the U.A.E., of which Dubai is a prominent part, sales are expected to grow 8% year-over-year to more than $61 billion in 2017, according to Euromonitor International. The market-research firm expects the U.A.E. market to expand at about the same rate every year to reach roughly $84 billion by 2021. That is more than double the annual U.S. growth rate.

By contrast, malls in the U.S. are struggling to stay open. U.S. retailers–facing increasing competition from online sellers after years of overbuilding–have closed stores at a record pace after the boom years of the 1990s. More than 8,000 stores are expected to shutter this year.

Dubai’s malls aren’t immune to the forces buffeting Western retailers.

E-commerce, which according to Euromonitor accounted for roughly 3% of all sales in the U.A.E. last year, is growing in double digits thanks to a large population of young people, expanding internet penetration and high levels of disposable income in the region. That growth has drawn global giant Amazon.com Inc., who earlier this year acquired Dubai-based Souq.com, one of the largest e-commerce businesses in the Middle East.

Malls in Dubai also have to contend with the sharp drop in the price of oil, the biggest revenue earner for many of its big feeder markets such as Saudi Arabia, which has weighed on regional consumer sentiment.

But the key difference between the U.S. and Dubai is that malls here are still a popular place to go, in no small part because of the searing heat. With temperatures soaring beyond 100 degrees Fahrenheit for months on end in most parts of the Middle East, Dubai’s malls have become modern-day oases, drawing both people from the region and expats that make up a big chunk of the population.

“It keeps them busy during the summer,” said Iranian Leila Kasraie, 44, while dropping her children, Sam, 6 and Kia, 5, for skiing lessons in Mall of the Emirates, which also has an enclosure for penguins. “Will now have coffee. Shop,” said Ms. Kasraie, holding a Louis Vuitton bag bought from one of the Dubai malls. “Wish I could come to the malls everyday.”

Dubai already has about twice as much retail space per capita as London, according to the global real estate services firm JLL. And yet to cater to the expected growth in demand, especially ahead of the World Expo in Dubai in 2020, developers are looking to expand retail space by a third by the end of 2019, according to JLL.

“Malls in Dubai are just not about shopping,” said Andrew Williamson, the head of Middle East and North Africa retail at JLL. “Where else in the world can you find something for everyone in the family?”

Earlier this month, Union Properties, a Dubai developer, unveiled plans for a roughly 1 million square-foot mall featuring a 250-meter indoor velodrome, a 700-meter indoor elevated running track, an Olympic-sized swimming pool and a 17,000 square-foot gym. It will also be home to a classic cars museum. Visitors, of course, will be able to shop and dine at the mall, the company said.

Dubai’s “bigger is better” ethos helped transform it from a tiny fishing village to a trade and tourism hub. The city is home to the world’s tallest building (Burj Khalifa); a palm shaped man-made island that has several luxury hotels; and it is building the world’s biggest Ferris wheel that will eventually dwarf the London Eye. Its police mind the streets in a fleet of cars that includes Ferraris and Lamborghinis.

State-owned Emirates Airline funnels millions of passengers every year through its hub in Dubai with many of them stopping over. Dubai’s tourism department actively promotes its malls, too, through discount festivals with raffle prizes that include luxury cars and exotic vacations or events.

Hundreds of people gathered last month for a concert featuring Arab pop star Balqees at the Mall of the Emirates. The Emirati singer–belting out her chart-topping numbers–was a star attraction for the mall as it promoted a six-week-long annual Dubai shopping extravaganza.

At Ibn Battuta, a themed mall named after the famous 14th century traveler, shoppers can follow his historic journey across countries such as China, India and Egypt.

At Dubai Mall, people can test their flying skills on the largest passenger jet in the world–the Emirates A380 flight simulator.

“The kids want to go see the aquarium. I want to shop,” said Kathy Shungu, who was visiting Dubai Mall with her husband and three young children during a two-week holiday from the Democratic Republic of Congo.

“Very, very nice,” she said. “Like a paradise.”

Write to Nikhil Lohade at Nikhil.Lohade@wsj.com

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Credit: By Nikhil Lohade