Hi folks,
This is actually a dependency issue in Ubuntu 14.04.2 LTS if freshly installed from a 14.04.2 media - before anyone asks, yes, the point release and the fresh install are important aspects here : the graphics stack installed by default has changed in 14.04.2, and it includes backported Xorg and drivers from the newer releases of this distribution.

Unfortunately, the backported packages break dependencies for a lot of development packages, some 32-bit ( <package>:i386) packages, a few more specific ones. 32-bit SDL2 is one of these. This library is required by many recent GOG games.

Previous point releases install media (14.04, 14.04.1) and 14.04.2 updated from 14.04.1 are not affected. A freshly installed 14.04.3 should not be affected either.
I'm afraid, however, that the Mint release based on Ubuntu 14.04.2 - 17.2 LTS Rafaela - is affected.

The issue has been known for a while, you can check its status here:
https://bugs.launchpad.net/ubuntu/+source/mesa/+bug/1424466

From what I gather, it is a packaging bug, but might be tied into APT dependency resolving logic.

The only known workaround on Ubuntu is to upgrade to a newer version (15.10 preferably, but note that GOG games are not officially supported for this version).
We do not know of a reliable workaround for Linux Mint 17.2 Rafaela, and we cannot confirm yet that updating to 17.3 LTS RC Rosa helps with the issue. Some newer backported Xorg and drivers might need to be installed, but APT might also ask to remove most of the graphics stack and leave you with a TTY session on reboot.

If anyone can try a Linux Mint 17.2 to 17.3 upgrade then let the support team know if this allows to install the following package, that would be perfect - we will also try it our test lab, of course :
libsdl2-2.0-0:i386

If you ran into the issue, don't forget to mark yourself as affected on launchpad, on the bug page mentioned above, and add a comment about your case being about libSDL2 32-bit.

I hope this helps.

For a game that only needs 32-bit SDL2, adding the library to the "lib" folder is not a big deal, but for games that need a number of other dependencies related to SDL2 (for example, check the list of deps for The Witcher 2), this quickly becomes a hassle.

Please keep in mind that our games are tested on Ubuntu 14.04 (and Mint 17), and switching to other, unsupported distributions might lead to issues caused by library discrepancies (especially ones affecting glibc).

I personally use Ubuntu 15.10 as my only operating system.