You'll never guess who's to blame.
Link from The Legend of Zelda pouring one out

Update May 27 at 2:00PM (ET): According to several sources, the issue isn't with the Dolphin Emulator per se, but rather the fact that the Dolphin team includes the Wii decryption key, aka: Wii common key, with their releases of Dolphin. This is obviously a big "no-no" as those are Nintendo property and are used to break DRM for Wii titles.

You can see at least one take on this from Modern Vintage Gamer on YouTube starting at the 4:43 mark of his video.

It has also been said by a person that was officially working with the Dolphin team that it was not Nintendo that initiated the takedown process, but rather Valve. In this Mastodon thread, Pierre Bourdon says that "to the best of his understanding" Valve contacted Nintendo to get their opinion on Dolphin being on Steam. Nintendo essentially responds with, "We think it's bad and that it violates the DMCA anti-circumvention provisions. Please take it down."

Furthermore, the statement on the Dolphin blog has been altered ever so slightly since this story was originally posted. It now says, "We were notified by Valve that Nintendo has issued a cease and desist citing the DMCA against Dolphin's Steam page(...)." This seems to suggest that an actual DMCA was not issued but rather it was a threat of a DMCA if the page wasn't removed.

Original story: On March 28, 2023, the team behind the Dolphin Emulator announced that they were going to release their program through Steam. Dolphin Emulator is a piece of PC software capable of running totally legitimate and legal copies of GameCube or Wii games that you presently own and have you yourself dumped onto your PC. It was also obviously capable of running homebrew software that was designed for the GameCube or Wii.

Ever since its announcement in late March, Dolphin had a whole Steam page setup and everything. It persisted for the past couple of months now before the entire page was quietly removed. And I bet you'll never guess why it was pulled from Steam.

Right, yeah. You got it. It's Nintendo. Of course it's Nintendo.

According to a new post on the Dolphin Emulator website, Nintendo issued a DMCA takedown request for Dolphin's Steam page. As a result, Dolphin's future on Steam is now "indefinitely postponed."

It is with much disappointment that we have to announce that the Dolphin on Steam release has been indefinitely postponed. We were notified by Valve that Nintendo has issued a DMCA against Dolphin's Steam page, and have removed Dolphin from Steam until the matter is settled. We are currently investigating our options and will have a more in-depth response in the near future.

We appreciate your patience in the meantime.​
I think most people probably saw this as being the inevitable outcome ever since the Steam release was announced. Nintendo is very predictable when it comes to this sort of thing.

Still, Dolphin isn't gone from the Internet or anything. Dolphin continues to be a free and open source project with or without being on Steam.