The tech exec is now wealthier than Mark Zuckerberg and Jeff Bezos, with a $250 billion fortune—but he’ll have a hard time dethroning his close friend Elon Musk.

David Ellison will soon take over as the entertainment giant’s CEO — but his mogul father, Larry, put in the $6 billion to buy it.

For decades, Larry Ellison reveled in being the Silicon Valley executive who really knew how to have a good time. He spent as much as $200 million building a Japanese-inspired imperial villa near ...