The demo version starts up fine for me, without any winetricks.
All I did was extract the zipped file to the Program Files directory of my test
wineprefix. I followed the instructions in
"1-Installazione_Attivazione.pdf" (with the help of Google Translate)
to log in. On the next screen I selected demo, and the app started.
Since I don't know the app or speak Italian, I have no idea whether it's
working as it's supposed to, but clicking on things does produce a response,
with no obvious errors.
I got exactly the same console messages as you.
What exactly is not working?