Because they operate on a very outdated understanding of how the world works. In their mind they own the games, they made them after all. The people "buying" the games don't really buy them, they just get a copy of the software and the license to use that copy. That license is limited in what you can and can't do. You can play them by yourself in your own home. You can even play with other people if they are physically in your own home. However if you want to do anything beyond that, it's outside of the license and thus not allowed. If you want to put on an event featuring their games, you need to apply for a license to do so and probably pay Nintendo for that license. Nintendo wants to limit the license even further lately, limiting playing inside your own home to their rules and limiting resale of the game (license).

This may sound crazy, and it is, however this is very much how music still works. And how movies and TV series used to work, and partly still do. It's a limited license for enjoying the media in your own home only. Technically when you throw a party, you would have to apply for a license to play the music you already own. When money is involved, like a bigger event and you don't play by their rules, expect to get sued. This is why the entertainment industry is so huge and the people in the top make so much money.

In the West we've accepted this doesn't apply to video games for the most part. Copying the game is a no-go, but using a game for entertainment purposes is allowed. When a streamer plays a game, they add enough of their own value for it not to be considered a violation. Even at large events, it's usually allowed. Although depending on the context, often license deals are made for the really big events.

There's gray areas as well, such as game modding or using the assets of a game to create a new game. This is also usually accepted, with services like Steam activily supporting mods and such. Most game devs like it when a community forms around their games and support mods. But not Nintendo, they hate this. They go after anyone doing this. Famously almost destroying the careers of people playing modded Nintendo games for entertainment. (Especially SMW romhacks). And people have to go through all sorts of hoops not to attract the eye of Nintendo (like how Ship of Harkinian does things). Another gray area is music in video games, usually that music has a rather open license. But not always and services like Twitch have made deals with the music industry in order to keep existing. That means upholding things like DMCA and muting or even disabling videos which contain copyrighted music. One recent example of this is Death Stranding, which contains so much copyrighted music it's problematic for everyone involved.

It has taken a very long time for the music industry to get around to the concept of streaming music. And even then the license is super limited and people don't own the music they pay for. Same for movies, TV series and other media. It has made them rich for decades, why give that up? Nintendo has always had the same mindset when it comes to video games and aren't going to change.

Personally I don't know why we put up with the BS system for music and other media. Especially the length of time for copyright these days. But large companies like Disney have so much power, it isn't going to change quickly. I feel the only reason we have music streaming at all is because the piracy got so bad they had to. And even then they fought it hard, demanding tens of thousands of dollars from little Timmy who downloaded a Metallica song.