Valve’s legal team got worried about hosting that (as hosting circumvention tools in the US is a direct violation of the DMCA, even if the tools are created by third parties), and reached out to Nintendo
Nintendo did their usual thing and said no (because they wrongly believe all emulation of their hardware is illegal, except if they do it), but in this case correctly identified the circumventing nature of Dolphin
Valve pulled down the Dolphin page on their own, without a legal demand from Nintendo
Valve continues to host RetroArch and the various cores, so it’s not like they’re opposed to emulation in general. The ability to copyright “magic numbers” in the US (Valve is an American company) isn’t up for debate, and it would also put them in violation of the DMCA, so it’s not hard to see why Valve would be worried about this specific emulator.
As for Dolphin, they have options:
they can choose to keep shipping as-is, without being on Steam, as they host from a non-US site with looser copyright laws
they can choose to not support encrypted payloads, and require that users supply independently-sourced decrypted games
they can require users to enter their own decryption key they dump directly from their consoles (which, realistically, means that users would get one off the web separate from Dolphin) and use a dumped system BIOS, which would fully emulate the “real” decryption process