Played about an hour so far of Kane & Lynch Dead Men using Proton and overall it worked great. You will need to use WINETRICKS/PROTONTRICKS to install some components, namely d3dx9_31 and d3dx9_34 from the 'Install a Windows DLL or component in the tricks menus. Once that is done it works without issue.

OS: Manjaro
Kernel: 5.15.50-1
CPU: AMD Ryzen 7 5700G
GPU AMD Radeon RX Vega 56
Mem: 32G

Works for me :D

Using PlayOnLinux. Wine 6.15 32-bit.

Sys: Linux Mint 20.1 Cinnamon
Kernel: 5.13.0-52-generic
Proc: Intel© Core™ i5-10300H CPU @ 2.50GHz × 4
Ram: 16GB
GPU: NVIDIA GeForce GTX 1650 v 470.129.06

PS. Not exactly. The game still quits with error after each chapter is finished. My progress is saved and I can restart the game and select a new chapter from the menu, but it's still a bit frustrating to make it after every chapter.