Aren't they obligated to shut it down in order to protect their IP rights? Copyright law is super complicated to me but that's my understanding of it.
Yes, and this is really all that matters at the end of the day. Failure to defend the copyright (or even challenge potential infringement of it) could lead to a ruling down the road that Nintendo is abandoning the copyright. If you allow someone else to use your intellectual property unchecked, the next person who wants to use it has a much stronger case. All it takes is allowing one to set a precedent that could come back to haunt you.
Nintendo MUST do this to maintain control of their IP. Saying "yeah we see that game out there, good job" and doing nothing to defend the copyright is essentially an invitation for others to use the IP as they wish.