No, you're not a lawyer. So I'll make this simple. The quoted regulatory provision is just that - a regulatory provision. Not a statute. And it regulates, as clearly stated, "aircraft operator[s]." Not passengers, aircraft operators.

So it in no way obligates any passenger to accede to the demands of a TSA gate-checker. Can your airline refuse to allow you to board because you haven't complied with a TSA screening demand? Perhaps, but that's between you and your airline. And I'd certainly argue that the airline (although it may be able to deny you boarding because it doesn't like the color of your shirt) cannot legitimately deny boarding due to its inability to "ensure that the individuals or property have been inspected by TSA before boarding" - given that you had to have been inspected in order to reach the gate area.

And it doesn't have to. So long as there is other law that prohibits gate screening, it is prohibited. In this case, that "other law" would be ones constitutional right to be free of unreasonable search and seizure.