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Hmmmm. I'm unable to replicate it, but a cursory search is saying that it's a fairly common issue. 

A couple of fixes I've seen mentioned are trying to run it in windowed mode (assuming that the launcher runs), and making sure that the /LIN_Tala_KickstarterDemo folder is in the same place as the x86 & x86_64 files.

I'll keep looking, though.

Aside from that, I'll start upgrading everything into the latest Unity version. It'll take some time, and I don't have the chance to start it tomorrow. Hopefully that'll work.

Do you have a preferred email that I can send a build to when it's done?

I've just played on an Ubuntu machine. It's a really great demo, congratulations! Waiting anxiously for the complete game and contributing on kickstarter as soon as possible!

I've tried earlier on a Linux Mint, there was the bug. Since linux mint is ubuntu based and a really similar OS, i guess it can be some video card problem. You can send me any build update to marcoaasilva AT gmail...

Thank you! I'm glad that you found a way to get it working and that you enjoyed it! 
I'll keep an eye out for ways to get it working on Mint, cheers!