Err, except it stopped working again.
I ran tech-setup as suggested, and it updated and the app launched. I quit it, then tried to re-launch it again, and again, nothing actually happens. Looking into it, ~/.itch/itch-setup has literally become a zero-length file:
mjog@blanchefort:~$ ls -l ~/.itch/itch-setup
-rwxr-xr-x 1 mjog mjog 0 Oct 10 18:12 /home/mjog/.itch/itch-setup