This game won't run on Ubuntu 19.10, when I try running it in a terminal I get

./Mable_PC: error while loading shared libraries: libcrypto.so.1.0.0: cannot open shared object file: No such file or directory

To install libcrypto.so.1.0.0 on Ubuntu (which should be included in libssl 1.0.0) you could try:

sudo apt install libssl1.0.0 libssl-dev

If it is already installed maybe give a simple reinstall a try with:
sudo apt install libssl1.0.0 libssl-dev --reinstall

Had the same Problem on Debian 10. There you cannot install libssl1.0.0 from standard repositories. Only newer versions.

Most easy solution is to download the Deb-Packages manually from:

packages.debian.org/jessie/libssl1.0.0
packages.debian.org/jessie/libcrypto1.0.0-udeb

You need to select your architecture. Probably "amd64". Once downloaded retrieve the following 2 files from the "data.tar.xz" archive inside the deb-package and copy them to the correct place. Open the deb-package with your standard unzip-program, NOT for installation. You will need root priviliges aka "sudo" to copy. You can use the following commands in the terminal.

sudo cp <your folder where you unzipped the data.tar.xz of libcrypto>/usr/lib/libcrypto.so.1.0.0 /usr/lib/
sudo cp <your folder where you unzipped the data.tar.xz of libssl>/usr/lib/x86_64-linux-gnu/libssl.so.1.0.0 /usr/lib/x86_64-linux-gnu/

I'd only add a bit more to ChoooChooo's post:

If you feel funny about adding "old" library files to your root's usr/lib folder, you can also do the following after downloading and extracting the files:

1) Go to the Mable the Wood's "game" folder (usually $HOME/GOG Games/Mable the Wood/game)
2) Create a directory "lib" (either with terminal or gui) ($HOME/GOG Games/Marble the Wood/game/lib)
3) Find the two ".so" files you extracted, cut and paste them into that "lib" folder
3) Go up one directory to the "Mable the Wood" folder ($HOME/GOG Games/Marble the Wood)
4) open the "start.sh" file with your favorite text editor
5) After the "#initilization" code and before the "#game info" code, copy and paste this code:

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:./lib

6) Save and quit the text editor
7) initialize the game using the "start.sh" file. Should boot right up

Thank you ChoooChooo for the links!

For anyone using Ubuntu 20.04 (or variations), the old version of libssl1.0.0 can be found here.

The file can be unzipped as ChoooChooo says.

I would also do as TinMonk suggests and "install" it locally to the game. Though I would add a minor tweak on step 5, quoting the right-hand side of the expression, just to be on the safe side:

export LD_LIBRARY_PATH="$LD_LIBRARY_PATH:./lib"

I know, the post is quite old, but here another way to solve this.

GOG has a script in support/gog_com.shlib, which is loaded by the start.sh script. This script has some functions to start the games in an "common" way.

The function execute_game() could be used instead of starting the binary directly. It has 6 arguments:
bin_32, bin_64 - These are the name of the binaries of the game, as 32 or 64 bit.
bin_path32, bin_path64 - Probably the directories of the binaries
lib_path32, lib_path64 - Here is the solution, the place to put extra libraries the game needs in that architecture.

So here the steps (again, but different):
1. get libcrypto.so.1.0.0 and libssl.so.1.0.0 as in the other responses
2. create the directory game/lib64 (I have a 64 bit version of the game)
3. copy the lib-Files into the game/lib64 directory
4. edit the "start.sh"-script:
4a. comment the line "./"Mable_PC"" (put a # in the beginning)
4b. add this line after: execute_game "" "Mable_PC" "" "." "" "lib64"
5. save the script and run the game :-)

I hope GOG will correct this.