When the Knicks perform poorly — as they often have under Mr. Dolan’s ownership — fans excoriate him. Politicians and bureaucrats castigate him for leading a company that enjoys enormous tax benefits while insisting that he will not financially contribute to the renovation of Pennsylvania Station, the rail depot that sits dank and dark beneath the Garden. He is entangled in a protracted public fight with a revered athlete, and uses facial recognition technology to ban from his venues people whom he says are adversarial toward him. Fans holding signs that say “Sell the Team” risk being booted because, Mr. Dolan said, they violate a code of conduct barring the harassment of the arena’s workers, including him. “I am an employee,” he said.

This month, with the Sphere set to open, he is approaching one of the most pivotal moments of his professional life. “The entire thing is a huge bet,” he said. In interviews, those closest to him stressed that the Sphere is wholly a Jim Dolan creation, a big gamble that places him outside of his father’s shadow and, perhaps for the first time, without the benefit of the safety net that owning some of New York’s most beloved institutions has provided.

“This is something he has done,” said Joe Lhota, a former senior Madison Square Garden executive who is on the board of the Sphere’s parent company. “It’s not something he inherited — it is him bringing his vision to life. It is totally, 100 percent his vision.”

Since the exterior of the Sphere was lit in July, social media has buzzed over the changing digital displays of fireworks, basketballs and even a 360-foot-tall eyeball that can be glimpsed from hotels along the Strip. Once guests experience the immersive visual and sound effects inside, Mr. Dolan believes the Sphere will become a premier venue for music and video productions. He hopes to build replicas around the world.

But the Sphere’s success is far from guaranteed. And no matter the excitement over his project in the desert, back home in New York, anger stoked by his perceived highhandedness is bubbling over.

He tried to push through the worry and let it embolden him, as he had seen his father do when he was creating HBO and bringing cable TV to New York and some of its suburbs.

When he saw an opportunity to assert greater control, he grabbed it. Earlier this year, as costs were spiraling and 2,400 people per day were working on-site to ready the Sphere for its scheduled opening, Mr. Dolan fired the project’s top executives and took charge — “Managed it down to the invoice level,” he said.