That's an error (or a typo). Those companies aren't "headquartered" there, but they are incorporated there.
The typical large American public company is incorporated in Delaware, with their stock listed on an exchange in New York, and headquartered wherever they actually do their business: San Francisco or Houston or Chicago or Atlanta whatever. Delaware and New York monopolize their respective segment of the business of the administrative paperwork of being a registered company. As another example, older companies that have physical stock certificates mostly have them locked up in a vault in NYC, with the ownership of the certificates just changing over in a ledger with every stock trade (millions per day) without the actual paper certificates being touched.
In my humble opinion, just as "no taxation without representation" is a thing the gov should abide by; "no representation without taxation" is probably good too. If these company's want to vote, have them pay 50% of all the money they every make to taxes.
Actually, not even then. If they want to vote, even if they paid 99% of their profits towards taxes to vote it would be a bad idea.