Bought my first game from GOG today, the Linux version of Shadowrun Returns. I'm using Fedora 23 (64-bit), so it was a bit of a gamble, but surprisingly I got it to work without having to resort to Ubuntu libraries. I know that GOG only supports specific versions of Ubuntu and Mint, and that's fine, but since there is no refund if a game doesn't work on my distro, it would be nice if was possible to post success/failure reports for purchased games, not only reviews. Just a suggestion.

You could start a "Works (or not) on Fedora" GOGmix:
https://www.gog.com/mix

Or simply post a thread on each game sub-forum with "Fedora" in its title, so it could be found easily by whomever would like to know if it works on this distro.

Joined in 2013 and bought your first game only today? Better late than never I guess :-)

Unless you're using a very old distro, most Linux games on GOG will run perfectly fine on other distros, GOG simply focused on Ubuntu/Mint because they are the most popular.

I often test different distros (such as OpenSUSE and pure Debian) on my other PC and games run just fine. That said, vv221's suggestion is a great idea.

True ;)
Linux comes in a huge variety of distributions, but under the hood the same tools are often used. While GOG claims to support Ubuntu & Mint only, if a game run on a said Linux distro it will most likely run on any not-too-exotic distribution.
The fun part begins when you need to track down dependencies that are not named in a same way from a distro to another…

I suppose you could add a table to the GOGWiki page of a game, sort of like AppHQ does for Wine.
Although any officially supported Linux game should work on pretty much any distro, even if GOG has picked only one to support.