In this context, "but not otherwise" means "but not in any other way"
Taken from wikipedia:
Moral rights are rights of creators of copyrighted works generally recognized in civil law jurisdictions and, to a lesser extent, in some common law jurisdictions. They include the right of attribution, the right to have a work published anonymously or pseudonymously, and the right to the integrity of the work
With respect to the section of the Creative Commons license you are referring to, this means that if you use a work published under the license, you don't get moral rights over the work as if you were the original author. It further states in the section that the author of the work (the one who put the CCv4 license on the work) agrees not to invoke those rights onto you - the user of the work - in order to not interfere with your ability to use/publish it, but that's it.
In essence it's saying that moral rights stay with the original creator, but will never be enforced on you in a way that prevents you from using the work in the way that you want (which in theory can be any way, depending on what variant of the CC you are using (CC0/Public Domain, Attribution only, share alike, non-commercial or no derivatives)).