It's told very clearly on both the project's website and in the linked video that they consider the Scheme language to provide a more hackable interface for package specification and management. It's also demonstrated that it all integrates very nicely into Emacs.

On top of that it's also stated in the comments here, by a Guix developer, that while having a DSL for package specification is nice, they think having a whole general purpose language for it is better.