I just tried running a Unity game on SteamOS, and I have the same issue. As you have found out (I saw your post on the SteamOS forums), the game is not finding SDL2.
On SteamOS, SDL2 is part of the steam-runtime. You can try to run the game within the runtime by issuing the following command on your SteamOS machine:
sudo /home/steam/.local/share/Steam/ubuntu12_32/steam-runtime/run.sh ./<YourGame>
Running this on our side resolved all the DllNotFoundExceptions, but we still don't have any audio. We are looking into the issue.