************************************ NEW Fix
To fix on Steam Deck and allow the game to start normally:

1. install the game normally on the Deck, don't launch the game.
2. Bring up properties for the game, choose compatibility, select "force the use of a specific steam play compatibility tool", choose "Steam Linux Runtime 1.0 (Scout)"
3. drop to Desktop Mode (hold power button for 2-3 seconds, select "Switch to desktop")
4. create a folder called "Remote" in the following path:

Home>.Steam>Steam>Userdata>(Your-unique-user-id)>251710

5. Save the below line into a file called meta.dat in that "Remote" directory you just created.

HExhdGVzdFNhdmU6MSxFYXN5U2NvcmU6MCxNZWRToAoDSGFyZIALATAs

Just copy that line, save it into a file called meta.dat (make sure the file extension is .dat NOT .txt!) and put that file in <Steam-folder>/userdata/<user-id>/251710/remote/

That should be all it takes to get the game running on Steam Deck. The next time you launch the game it should start normally and drop you in the main menu after the Dev / Publisher logos screen; no more black screen with music.

This works for Steam Deck, but you still have to go through the Compatibility Mode + As Administrator steps to fix a Windows installation of the game as far as I have tested.

***************************************
##### Nov 2023 UPDATE #####

I had to redo the process for the OLED Steam Deck and the above steps did NOT work on the first try.

In short; if it doesn't work; uninstall the game, reinstall it. Try again the above steps again without launching the game.

My suspicion is that when you first install there is no "Force Compatibility" mode selected. So if you apply the fix and try to test it by launching the game, I believe something similar happens that others have described when fix the game in Windows, where if you launch from within Steam's UI, it breaks the game somehow and you have to remove the game and apply the fix again in order for it to work again. My only guess is that has something to do with Registry Keys that are created the first time you launch the game.

If you do have to start over, you might need to go into Home>.Steam>Steam>SteamApps>Common>ChainsawWarrior (game binaries location) as well as into Home>.Steam>Steam>Userdata>(Your-unique-user-id)>251710 and delete the contents as well.

So when the steps don't work and you are tinkering, and you eventually select a compatibility mode, then decide to start over, that compatibility mode is retained from uninstall / reinstall, so the same steps above seem to immediately work after you've done that.

This all seems to work best if you choose "Steam Linux Runtime 1.0 (Scout)", and so I have added that to the above steps.

*********************************** OLD / Manual Fix

Or alternately to fix on Steam Deck and allow the game to start normally, you can

• apply the Compatibility Mode fix on a Windows PC
  
• start the game as normal
  
• start a new game
  
• create save data by simply saving the game
  
• copy this save data meta.dat to the game's save location on the Steam Deck

That's it. Someone may choose to upload the necessary save data and that may work as well See new steps above but with these original steps you will create your own meta.dat - the save files are not necessary to fix the game on the SteamDeck, only meta.dat.

Performing the above steps creates two files and a folder in the game's save location and copying that to the Steam Deck fixes the issue.

Save Location for Game according to PCGamingWiki:
<Steam-folder>/userdata/<user-id>/251710/remote/

After completing the above steps for the compatibility mode fix in Windows, you should find the following files in that location:
/<user-id>/251710\remote\meta.dat
/<user-id>/251710\remote\save1.dat

Simply copy meta.dat to the save location on the SteamDeck.

/home/deck/.local/share/Steam/userdata/<user-id>/251710/remote

The save files are not needed, but you will need to create the "remote" folder in that location.

I used a spare microSD card as that seemed to be the simplest option to me.

I am not a Linux expert, so I can't advise further on the best way to accomplish that, but to get you started you can drop to the desktop on the Steam Deck by holding the power button for 2-3 seconds and clicking "Switch to Desktop", and the file explorer is called "Dolphin".

I inserted microSD card into the Steam Deck, a prompt popped up to mount/browse the disk, copied meta.dat to the game's save location on the Steam Deck, used the "return to game mode" desktop icon returning me to the normal Steam Deck User Interface, and the game launched normally from there.

It's working for me so I'm probably not going to mess / experiment with it anymore. The game seems very friendly with the touch screen so far. Have fun!

One Important Note:

In my earlier troubleshooting I had selected "Proton Experimental" as the "compatibility" --> "force the use of a specific Steam Play compatibility tool" option so I know the Steam Deck is running the Windows version through proton rather than the Linux native version. I'm fine with that, it's working but it is likely a key element of these steps fixing the game on the Steam Deck as the save information is being created by the Windows version - the remotecache.vdf includes a line that reads "ostype" and the value is 16 - that undoubtedly will differ for a file created with the Linux binaries.

I confirmed that after you apply this fix, if you remove the "force the use of a specific Steam Play Compatibility tool" option it will run the Native Linux version and it will launch and it will play but it appears that there will be No Sound. But if you choose the "Steam Linux Runtime" compatibility option it seems to run the linux binaries as expected and the sound will work too. So keep these things in mind.

Hopefully this helps someone.

Game on.