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(+1)

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 click itch-setup in the Downloads directory). 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.