Hi, thank you so much for fixing this so quickly! I can confirm that the itch client now unpacks the installation properly. I can also launch and play the game without issues (at least, none that I can see). I am using Debian 10 on a 64-bit computer, but I have multi-arch enabled so I can install and run 32-bit programs as well.
There is only one small issue that I have not been able to resolve. Launching the game from the itch client leads to extremely garbled sound output. However, if I launch the executable directly from my file manager or from a terminal, the audio is fine. I don't know why using the itch client causes this, but I'm happy to help you diagnose this further if you are interested in fixing this.
Edit: changed some wording to be more clear