Ahhh. That is what is written in the desktop shortcut, if you let steam create one.
The itch app on windows launches with
itch-setup.exe --prefer-launch --appname itch
So yeah, I would assume you might be able to supply an appname different than itch. I could not do it while testing for a minute. So maybe not. It tries to run name-setup, if write name instead of itch. But it sure looks, like it should be possible.
So what we want is a way to launch games without opening the itch app interface.