The Yun Mini appears to be exclusive to Smart Projects, so they seem to be capable of developing products without Arduino SA.
I guess that forks of Open Source software are quite common and perhaps inevitable, e.g. OpenOffice/LibreOffice. In those cases, there are no direct sales involved, and there is no dispute over the name. Although SCO sued over the ownership of Unix, it always seemed doomed to fail.
The dispute over the Arduino trademark is a simple legal question, but in principle anyone could fork the entire Arduino product line and brand it with their own name. Even if Smart Projects were forced to change their brand name, they can hire programmers, web designers etc to continue independently of Arduino SA.