Works out of the box
Played perfectly fine out of the box, both DX9 and DX11 modes

MANGOHUD=1 gamemoderun %command%
RADV_PERFTEST=gpl,nggc,sam

I just installed WMP11
I just installed Wine_GE-Proton8-26 from Heroic Games Launcher, installed the game from GOG and launch winetricks withing HGL and installed WMP11. It runs great, I haven't tested the Controller yet or multiplayer. WINECFG was set to win10 by default.. I hope it works also on Steam, probably if you add the same Wine I did using ProtonUP-QT, also make sure DX10 and 11 is set on game settings. My GPU is Nvidia 2060 as well as AMD.

Second report for this machine
It turns out that the issues I was having initially with this configuration was on my end and I misconfigured my system. After fixing the problems that I had the game now works perfectly. I hate posting again to counteract an earlier post here on proton DB but it is what it is. Either way, this time it ran perfectly without any tinkering or launch options required of any kind.

Totally Borked on Nvidia Manjaro
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; gamemoderun %command%
Simply fully borked. I run it on my steam deck all the time, just not on my main PC.

The only way I could get it to run was to install it using Heroric Games, then add it to my Steam library and launch it with Proton. Game runs perfectly with no issues.
I did try Heroric and GE-Proton but I only got to the menu and it crashes.
No launch options used.
I only have the Epic games version so had to install with Heroric, Launch through Steam. Not tried Lutris yet.

This game uses a launcher. For ease of use I recommend permanently altering the standard gamepad controls in order to allow mouse control on one of the track pads or with the gyro and mouse clicking. Alternatively you can hold steam button and use the trackpad as mouse at all times steam button plus right trigger is mouse click and steam button Plus right on the d-pad is enter. As a tertiary option, you can navigate the launcher and alter settings exclusively through the touchpad.
The game works flawlessly with graphic settings maxed and at native resolution for the steam deck with a flawless 60 frames per second at all times with literally zero stutters. The only consideration is controls and that's only because graphic settings and some other things like that are configured in a launcher window that only works with mouse input, not gamepad input. But if you've played around with the steam deck or the steam controller or really any kind of steam input any reasonable amount you should be well versed in these kinds of minor hiccups and how easy they are to bypass or work around. Overall the experience with this game is essentially flawless.

the intro before the main menu stuttered
the intro before the main menu stuttered
the mouse didn't move. But you play the game with controller or keyboard. So it won't actually matter.
The intro was very laggy but the game itself works very good.

Opening video doesn't work on Proton 8 so I used GE instead.
DirectX 10&11 option is still borked.
Works perfectly fine
PROTON_USE_WINED3D=1 %command%
I almost always need the wined3d flag on this config, you probably won't on yours
Works flawlessly ootb
No issues

cd "${STEAM_COMPAT_INSTALL_PATH}/launcher";gamemoderun %command%
Installed from Amazon Prime Gaming
Installed from Amazon through Lutris. Black screen or freeze on splash screen depending on wine/proton version. Targeted GSGameExe_DX9.exe and added as non Steam game. Forced Proton experimental. Added cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; gamemoderun %command% to launch options. Runs great through first levels so far. Solid 60 fps and no hiccups. Will update if any change or on completion.
Had to use Steam + Trackpad and Steam + R2 to navigate the launcher and configure the settings.
I still cannot pass the loading screen no matter what I try.
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
The loading animation works for a moment then the game freezes. Same, with or without the launch option.

Use of touchscreen/mouse is required in the initial launcher if you want to change settings. You can use the shortcuts without having to edit the layout to get past the launcher
- Steam + R Stick for mouse
- Steam + R Dpad for Enter (Play)
Use shortcuts to get past the launcher.
Graphic settings are outside of the game. By default, the trackpads don't function as a mouse and will require using the touch screen to adjust. Works great at 60 fps.
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
Just go into the game's properties > general and set launch options to:
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
Enjoy the game.

cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
Finally! I've waited eight years to play this. 🎉
At first my controller wasn't properly recognized, but that was probably caused by years of tinkering attempts. Deleting the Proton prefix (steamapps/compatdata/223220
) helped.
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; gamemoderun %command%
Game does not launch without additional config input
Yes works perfetc stable and fast, if you use the command "cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; gamemoderun %command%"
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; gamemoderun %command%
You'll have to add 'cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%' as launch option or you won't get past the loading screen.
Needs custom launch options, otherwise it will quit after the launcher closes when you hit Play!
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
Funciona con mandos (logitech f310 y xbox 360). En mi caso funcionan tanto en dx9 como en dx10/11. Gracias a la comunidad por el comando.
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%

cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
Had to use antimicrox to enable controller support.
Game worked well once I'd selected Proton 7.0-1 and added the launch option.
cd "${STEAM_COMPAT_INSTALL_PATH}/launcher"; %command%
The launch options have been identified in the github to the game: https://github.com/ValveSoftware/Proton/issues/1658#issuecomment-1046887271 With this it now runs flawlessly.
Die Startoptionen wurden im Github zu dem Spiel ermittelt: https://github.com/ValveSoftware/Proton/issues/1658#issuecomment-1046887271 Damit läuft es jetzt einwandfrei.

The Button Einstellungen(settings) gives an unhandled exception error. Spielen(Play) crashes the Game.
Although Game is set to English in steam launcher opens in German(my system language) .

Das Spiel lässt sich installieren. Nach dem Starten erscheint der Launcher. Das Spiel startet aber nicht.
Ich habe diverse Grafik-Einstellungen (Vollbild und Fenstermodus, geringere Auflösung, DirectX9 oder DirectX10/11 ...) im Launcher ausprobiert, aber das Ergebnis ist immer das gleiche.

steamtinkerlaunch
By default the game refuses to start, because of the wmv intro video!
This can be circumvented by
- extracting (cabextract) and copying "WMASF.DLL" and "WMVCORE.DLL" from Microsofts WMP10 Installer "MP10Setup" (removed upstream!)
- and starting the game exe "GSGameExe.exe" directly instead of the (forced) game launcher. This can be done easily by using steamtinkerlaunch
For details see this summary on the proton issue

The game is awesome - wonderful level design, great gameplay and audio in Ohrwurmqualität
I got it working (with substantial tinkering, but the game is worth it). I used the install script from lutris.net, tweaked it to use a hard-coded prefix, switched from fullscreen mode to windowed (to avoid having to hard-quit the X server in case the game crashes) and pressed ESC on the company splash screen. I guess the most important part is pressing ESC on the splash screen, but I'm not 100% sure. A ton of thanks to @GameOnLinux and @IronScyth for their support (on YouTube) in getting this working!
While tinkering with the installer, I switched to windowing mode to avoid having to reboot the computer in case the game doesn't start properly, and I never went back to fullscreen (too lazy).
When the computer enters sleep mode, the game seems to be crashing after a while (sound is still playing, but I can't get back into the game.