Sure, and like I say trademark is the one obligation they have. However, there has been no indication that protecting a trademark was the driving factor. The driving factor seems to be entirely that it involves Nintendo.

Furthermore, there would be no fight with Nintendo here. Nintendo have no real grounds to sue Valve, even if Valve ignored it. Rather, it almost plays out as if Valve hope to host Nintendo software on their platform - which doesn’t seem likely to ever happen.