They get the lions share of their money by sales and not by donations. They negotiate deals and contracts for money, they sell merchandise and/or license merchandise for sale, they research means of greater revenue, and they take a portion of the proceeds for their personal and organizational funding.
Just because they spend all their profit doesn’t make them a non-profit.
It has nothing to do with donations, unless you mean the revenue sharing between teams which goes through the NFL shell.. It has to do with the structure, and the structure is that the NFL shell retains nothing upon which to pay taxes on, and the funds are transferred to teams which do pay taxes on net earnings. Are you trying to argue that they should pay taxes on the money twice or more?