I run Fedora on my machine I am intending to game with (F28 atm). Sofar I have managed to make the launcher work, but took a rather ugly workaround that I think should not be needed.
The problem lies with the dependency on Ubuntu specific files and versions for libssl and libcrypto. The Ubuntu ones required here are older than what the oldest (from openssl-compat10 package) Red Hat packages up, and are NOT compatible. Symlinking via name was not doable (or for that matter copying the compat provided ones to the game directory). I had to go grab the Ubuntu deb package for openssl and snag the two files out and plop them in the game directory and load the launcher as follows:
$ LD_LIBRARY_PATH=./ ./Launcher
This could be avoided by including the needed files and using a shell script to load the launcher up. Valve does something similar with their runtime environment, includes all kinds of so’s for use just like this. As it seems that this is likely the only or on a very short list, inclusion would be a much saner and simpler way for people on !Ubuntu to use the game.