If I put the GPL in my software and add a file next to it that says "Also you can't use this software if you make more than $100k/year", I've pretty clearly added an additional clause that's incompatible with the GPL.
But I was responding to the comment upthread "You can add any message you want into your GPL program". If you add a message that says a user of the software must do something / must agree to additional terms / etc, that additional text is not compatible with the GPL. I'm not a lawyer, so I have no idea whether the result would be that the restriction doesn't count and the software is GPL'd, or that the software isn't viably GPL'd because the GPL+clause isn't a valid license for somebody to use.
For one thing, if the author provides the source with a GPL license to user A, and user A sends it to user B, user B has the software under a GPL'd license. The normal reason for dual licensing GPL/proprietary is so that user B can pay money to bundle the software in a non-GPL-compliant way. The author can stop licensing future releases under GPL, but they can't revoke the GPL on already-distributed software.
For another, this isn't what's happening here. GNU Parallel is released under the GPL, and the author is affixing what is debatably an additional term to the GPL'd release, under the claim that it doesn't count as an additional restriction because it's "academic tradition". By the same token, I can add a clause to my software saying that rich people can't use it, because it's "hippie tradition" to stick it to The Man.
The author of Notepad++ for example is famous for adding all kinds of statements associated with the software and in no way is that part of the license.
On the other hand, if your license.txt states to i.e. not use the software for evil aka JSON famously did then yes, it is part of the license.
