Not a historian, but I'm familiar with antitrust law and this case. Standard Oil, as a single entity, had actually been broken up before by an Ohio state court. After that, they moved to New Jersey, one of the only states at the time which allowed a corporation to own stock in other corporations (which is legal in every state today). At that point, Standard Oil was just a holding company which happened to own 34 different oil companies around the US. So, when Standard Oil of New Jersey, the holding company, was ordered broken up, the Court was basically saying "you can't own these 34 subsidiaries." Each one was already a standalone company in terms of its ability to operate. So Standard Oil of New Jersey complied by selling the individual subsidiaries to other investors/companies.

So, Rockefeller did not sacrifice any wealth. His company sold each subsidiary for its fair value and his company retained the value from those sales. However, the value of the entity as a whole did drop considerably due to the end of its retention of monopoly power.

Edit for some clarity: Rockefeller did not just sell for cash. He retained ownership in most of the individual companies, he just could not legally maintain a controlling interest, as the holding company had. I think he owned something like a quarter stake in many of the new companies, ones which would become Exxon and Conoco among others, so he became insanely rich as they grew.