I solved this for me by giving itch a wine executable to work with. Itch can download Windows games on Linux if a wine
command can be found at a location defined in the PATH
environment variable. I edited the itch desktop file to add the Steam Proton Experimental directory to PATH
by replacing:
Exec=/home/deck/.itch/itch %U
with
Exec=env PATH="/home/deck/.local/share/Steam/steamapps/common/Proton - Experimental/files/bin/":$PATH /home/deck/.itch/itch %U
After restarting itch through the desktop shortcut, I can download Windows games and add them to Steam using the regular “Add a non-Steam game to library” process and selecting a Proton version in the compatibility properties.