I haven't make any real progress, but now I'm almost sure the problem has to do with Flash: since I installed the game, the Steam client isn't able to display any video correctly. When trying to view a video on Greenlight I get a text error message instead: #text_need_flash_inclient. And if I try to view a video on the store, I this other message:
You need to have a specific Flash Player installed to view video content
in Steam. Please follow these directions to get the right version for Steam.
You will need this Flash player even if you already have the latest player for
your default web browser.
Even though I have the adobe-flashplugin package installed, I followed this instructions (which by the way seem tailored for Windows users, as I didn't find any Flash Player 11 for Other Browsers option) but all I got was a tarball with the same libflashplayer.so that was already installed in my system.
The funny thing is that videos on the Steam client worked fine before I installed Deadly 30. Could the game have messed up my flash configuration in any way?