I've updated to v1.32 with the game's auto-updater. (I've let it run in Wine for a few minutes, then killed everything, update seems to work, then I've restarted the game manually.)
I have then hosted a game with the "public" option active in the set-up. The game didn't appear on this website's multiplayer server list, even after several minutes, with constant page refreshing. Clones uses NAT punchtrough, so I shouldn't have to forward ports. I've forwarded UDP and TCP 9877-9878 nonetheless, and the website still didn't list the game.
Could someone double-check whether they can host and have themselves listed on the website as a server?
Starting the game alone records a play on the multiplayer history page, as desired, so the game does connect to the website.