RUN #1
Running Surviving Mars
./MarsGOG: error while loading shared libraries: libcurl-gnutls.so.4: cannot open shared object file: No such file or directory

Went to /lib64 directory and added the following...
ln -s libcurl.so libcurl-gnutls.so.4

RUN #2
Running Surviving Mars
./MarsGOG: /lib64/libcurl-gnutls.so.4: no version information available (required by ./MarsGOG)
./MarsGOG: /lib64/libcrypto.so.1.0.0: no version information available (required by ./MarsGOG)
Protocol error: bad 3 (Window); Sequence Number 5
Opcode (20, 0) = GetProperty
Bad resource 1210270872 (0x48234498)
at -e line 15.
./start.sh: line 16: 29365 Segmentation fault (core dumped) ./"MarsGOG"

The program started and went to main screen and then core dumped.

Has anybody experienced this? And how do you fix this?

Nobody?!??! :(

Hmm??? OK....Ok....ok....

Well... I have Surviving Mars working on a Fedora 28 system.

Care to tell us how?

I wasn't sure if anybody else was interested...

- Install steam if not already done...
- Modify the start.sh file to add the steam libraries..

# Actions
run_game() {
echo "Running ${GAME_NAME}"
cd game
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$HOME/.local/share/Steam/ubuntu12_32/steam-runtime/amd64/lib/x86_64-linux-gnu :$HOME/.local/share/Steam/ubuntu12_32/steam-runtime/amd64/usr/lib/x86_64-linux-gnu/
chmod +x "MarsGOG"
./"MarsGOG"
}

Works great!!!

I just experienced this on OpenSuSE Tumbleweed.
Tried the same remedy as you, but the game seems to need the GNUTLS version of libcurl, while SuSE and maybe others ship the OpenSSL version.
You can do without Steam however if you build the library yourself.

Solution based on this post by Amy_Stryke in another game thread: https://www.gog.com/forum/mount_blade_series/mount_and_blade_warband_on_opensuse_aka_fixing_libcurlgnutls

* install a suitable build environment (replace zypper with your distro's tool):
zypper install gcc libgnutls-devel
* download curl source package from https://curl.haxx.se/download.html
and decompress it
* in the extracted directory, compile it with:
./configure --without-ssl --with-gnutls
make
* the finished library will be in ./lib/.libs/libcurl.so.4.5.0 (depending on the version you compiled)
* copy the library to the game's installation folder into the "game" subfolder
For me, thats
cp ./lib/.libs/libcurl.so.4.5.0 ~/GOG\ Games/Surviving\ Mars/game/
* create a symlink so the game finds it:
cd ~/GOG\ Games/Surviving\ Mars/game/
ln -s libcurl.so.4.5.0 libcurl-gnutls.so.4

Alternatively, you can give the library the name the game expects (libcurl-gnutls.so.4) during the copy operation.
This did it for me.