Indeed, thanks for the quick reply.
IANAL etc. but I would keep my hands off that software:
1. The author requires the user to accept the GPL before using the software. However, the GPL states that agreement to the license is not necessary for the purpose of simply running the program. Agreement to the GPL is required only for performing all other activities by the license.
2. The user has to agree to additional licensing terms written down in an extra EULA. The provisions in the EULA conflict with the GPL, particularly the provisions in the EULA requiring the user to agree not to use the software for certain purposes. Most of those provisions are redundant, as most of those activities prohibited in those are illegal in most countries anyway.
3. The Section 7 of the GPLv3 restricts the restriction an author may apply to his or her software. It does not matter if those restrictions are written down in a separate license or not.
The author's intent is unclear, as both the GPL and the EULA contradict each other. The author should contact the FSFE Freedom Task Force in order to resolve the licensing issues: http://www.fsfe.org/projects/ftf/ftf.en.html