Steam built their own Linux distribution, are you wanting GOG to do something similar?
Like GOGnix? GalaxyOS?
Steam also includes "The Steam Runtime", which insulates Steam games from the underlying Linux distro by providing known copies of every library the games may depend on.
You know that's nothing new for (Linux) installers, right?
There are Linux installers which just use the global libraries and updates those if required, but there are also Linux installers which use local copies of libraries and uses them instead of the global libraries.
Both have their ups and downs;
1. If an installer uses the global libraries and doesn't get updated for a while, the globals may be higher versions than expected, with different code-hooks. This could make the game stop working over time, or even fail to install as its dependencies aren't met. But it does make sure the game runs on newer distros and can even run more smoothly or with higher quality than before when bugs in those libraries are patched out. It just takes some maintenance from the package-maintainer/game-devs.
2. If an installer uses local versions of libraries, it could lead to it running unstable on the system or even to it opening the system to attacks which had been patched out in the new global versions of those libraries. It will probably run for longer before running into issues, though, mainly due to not having to check for existing dependencies.
Even on Windows there are programs which use their own versions of, say, mono or other libraries. These programs then have the libraries' .dll files located within their installation folders. It's not purely Linux which has this "issue".