Yeah, so here we go, my third issue with the Linux port of Shadowgrounds... anyway, it turned out to not be that difficult to fix.
Shadowgrounds only really plays well with OSS, so you should run it through aoss, but that won't work in 64 bit. So here's the solution:
First, install alsa-oss (sudo apt-get install alsa-oss), then download this archive, extract it your game directory and run shadowgrounds-x64 from now on - easy as that. Download me
If you prefer to do this by hand, first download the alsa-oss package for i386 (from here), extract it (dpkg --extract alsa-oss_1.0.17-4_i386.deb alsa-oss) and copy the files in usr/lib/ to /usr/lib32/ (sudo cp alsa-oss/usr/lib/* /usr/lib32/). Now when you want to run the game, you should run it as:
1LD_PRELOAD="/usr/lib32/libaoss.so" aoss ./shadowgrounds-bin