There's no source for the claim. Here is all the New Yorker article says:
"That lucrative maneuvering is the realm of specialized attorneys, accountants, and money managers, many of whom work for family offices: in-house financial teams that typically include a dozen or so full-time attendants. Family offices, which have roots in nineteenth-century operations that served John D. Rockefeller and a handful of his peers, have proliferated in the past two decades, to at least ten thousand worldwide. They tend to have no public presence—Gordon Getty’s family office is known, inconspicuously, as Vallejo Investments—but by some estimates they control about six trillion dollars in assets, a larger sum than is managed by all the world’s hedge funds."
By some estates. Yeah ok. There's absolutely zero actual evidence to suggest the Getty family controls even a hundred billion in assets. No major wealth investigators (Forbes, Bloomberg to name two) in the past three decades has turned up such a large stash by that family.