I tried to link the latest build to my Steam-account and converted my key to that. It got accepted, downloaded, but when I started it would tell me basically that I don't own a key for the game. The log showed a non steam version, forcing a verify in Steam always showed >4000 files to be redownloaded, which wouldn't help, I did that just to make sure. Today I tried under Windows and after the download in Steam finished I got a requester to link the account, which didn't happen under Linux. The requester looked in game style, so I believe that requester is launched from PA, not Steam. As a sidenote, that requester doesn't support the "@"-symbol (German keyboard-layout if that helps, it took only letters and numbers) which would lead to problems if you haven't got an Uber-account already. I had, so that went fine from then on. Starting under Linux is now no problem, too, no redownload needed as it seems to have gotten the right version yesterday (even Log didn't really agree), just the Link between Accounts didn't happen. If all this is explained and a known issue, I wasn't able to find it via search and am sorry for wasting your time.
As is outlined by a sticky thread in the Steam Hub, you have to link your account on https://uberent.com/user/linksteam if you launch the game on linux. http://steamcommunity.com/app/233250/discussions/2/810938082193900075/