We have seen countless ( Well, not ACTUALLY countless ) fan projects get taken down by Nintendo based on copyright grounds.
Projects such as AM2R, Pokemon Uranium, Super Mario Bros X and many, many more were a victim of Nintendo and their defensive stance when it comes to their IPs. It’s very clear that they have gotten a lot more defensive throughout the years.
Super Mario 64 Online is a fan project that has been a long time in development, and one that has finally gotten an official release. However, as with every other fan project, Nintendo tried to take it down as quickly as possible.
The thing is… Super Mario 64 Online doesn’t include any copyrighted content in it. The download linked in the description of the video only contains an .exe file which when launched adds the online functionality ( Along with new playable characters ) to Super Mario 64
Based on this, Nintendo really can’t do anything about it. They may have taken down the trailer, but the link to the download still stands and can be downloaded by anyone.