Chivalry 2 isn't working on Steam Deck out of the box, it will hang on the launch screen.
Fortunately, thanks to Proton DB users, all it needs is a simple command line fix.
Copy and paste all of the following into your launch options for Chivalry 2 (in the game properties in Steam) and you will be good to go
eval $(echo "%command%" | sed 's/Chivalry2Launcher.exe/TBL\/Binaries\/Win64\/Chivalry2-Win64-Shipping.exe/')