This has not do with beneficial ownership of the underlying asset alone. Principals sometimes do not have that relationship. Asset ownership is a common way to benefit from a entity, but not the only way.
Specifically here Sam Altman does not own shares in the for-profit entity and non profit entities do not have shares.
I don't have direct knowledge on how OpenAI handles it, however it is not uncommon to do revenue sharing, or lease an underlying asset like a brand name (WeWork did this) from the Principal directly, or pay for perks like housing, planes etc, or pay lot of money in Salary/Cash compensation, there are myriad ways to benefit from control without share ownership.