Viewing post in How to play itch.io games on the Steam Deck comments
Take a look at this thread here: https://itch.io/t/694459/please-allow-installing-windows-versions-under-linux
Specifically, this reply from Fahrstuhl:
Put your Steam Deck into Desktop mode by pressing the Steam button, clicking Power and select Switch to Desktop. Open Firefox, download itch for Linux from https://itch.io/app and run the installer (double clickitch-setupin theDownloadsdirectory). Then right click on the itch icon that was created on your desktop and open with Kate, a text editor. There you replace the line that says:
Exec=/home/deck/.itch/itch %U
with a line that says:
Exec=env PATH="/home/deck/.local/share/Steam/steamapps/common/Proton - Experimental/files/bin/":$PATH /home/deck/.itch/itch %U
On the next start of the itch client in desktop mode, you can download and install Windows games.
That allowed me to install Windows games through the app.
Download Flatseal from the Discover Store. Go to the itch app in Flatseal, scroll down to Environment find the says PATH=... and replace the whole line with this
PATH=/app/bin:/usr/bin:/usr/lib/extensions/vulkan/gamescope/bin;"/home/deck/.local/share/Steam/steamapps/common/Proton -
Experimental/files/bin/" you can replace Proton - Experimental whatever Proton version you are using.