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

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"