do steam games run on linux already or something?

Oversimplification coming, but...

Most (modern) games can actually just run on Linux already, because Linux is where the best cross platform developer tools are.

Today, if a developer wants to publish their game to Windows, Mac, Android, Playstation, Nintendo Switch and XBox - the odds are strong that the developer is actually (possibly unwittingly) writing a Linux native game and then using an engine to port the Linux version to the other platforms.

The reasons for this are complicated, but mainly boil down to Linux being the simplest target to reliably build developer tools for - because every part of Linux is open and public.

Like do you only have to do that for non steam games?

If a game is purchased through Steam, Steam launcher knows enough to choose the best available version of the game for the operating system - whether the best version is the Windows executable running under wine/proton, or a native Linux executable.

Some have native Linux versions, while the rest can be "translated" (not strictly emulation, but the concept is close enough) via Proton, a translation layer that Valve introduced with the Steam Deck, which is itself running (arch btw) Linux. I'm not sure what the split is in the catalog, but the steam deck verified list serves as an indication for Linux (for Arch, at least) compatibility in general.

This is true for both Steam and non-Steam games - the developer or publisher might offer a native Linux version, but packaging is always a mixed bag. This proton trick allows you to run the Windows version with the same compatibility it would have on the steam deck, no matter where it came from.