Does Dolphin Emulator run on Linux?

Dolphin is developed for Linux as a first-class platform. The project's repository names Windows, Linux, macOS and Android, and a Flatpak is available from Flathub so it installs and updates like any other app on your system.

Everything you care about copies across. Your game files, memory card files and save states live in ordinary folders, and moving them from the Windows machine is a matter of dragging a folder. Controller settings and graphics options sit in the configuration folder and come over the same way.

One caveat on the Flathub package: it carries a notice saying it is community provided and not supported by the Dolphin project. It works, and plenty of people use it, but if something goes wrong the packager sits between you and the developers. The project also distributes builds directly if you would rather.

Wii motion controls are the other thing to plan for. Getting them to feel right still wants a genuine Wii Remote paired over Bluetooth, which is true on Windows too, but adapters vary in how well Linux gets on with them. Test yours before you commit.