Of course, the copyright holder can license as they wish. But the quoted terms of the GPL are in the license that the author is distributing with the software, so we can also follow the terms of the GPL and remove the extra restriction they just added. The author is trying to do contradictory things: add extra restrictions, but release under the terms of a license that allow us to remove those extra restrictions.

If they want to add that restriction, they cannot release it under the GPL; they need to pick another license, or modify the GPL to their liking and then call it something else (assuming the copyright terms of the GPL allow you to make a derived work of the license itself).

Wouldn't they still need to switch to a license outside the GPL family in order to add those restrictions, even if they're the sole copyright holder? Otherwise it seems that upon receiving a copy of the software, the user can just remove the additional restrictions, as specified by Section 7.