It's highly likely in my uneducated opinion that OpenAI will be told to adopt a standard corporate structure in the near term. They will likely have to pay out a number of stakeholders as part of a "make right" setup.
For a good point of comparison, until 2015, when public scrutiny led them to decide to change it, the NFL operated as a nonprofit, with the teams operating as for-profits. Other sports leagues continue to have that structure.