thi work for mi in debian 11

wget http://ftp.us.debian.org/debian/pool/main/libp/libpng/libpng12-0_1.2.50-2+deb8u3_amd64.deb

DIRGAME="$HOME/GOG Games/The Pillars of the Earth"


mkdir $HOME/tmplib
ar xv libpng12-0_1.2.50-2+deb8u3_amd64.deb data.tar.xz --output $HOME/tmplib/
tar xvf $HOME/tmplib/data.tar.xz -C $HOME/tmplib/
rm -f $HOME/tmplib/data.tar.xz



cp -rf $HOME/tmplib/lib/x86_64-linux-gnu/* "$DIRGAME/game/libs64/"
rm -rf $HOME/tmplib/

If you have Steam installed locally, it also may work to point to their libs:

export LD_LIBRARY_PATH="~/.local/share/Steam/ubuntu12_64/steam-runtime-heavy/lib/x86_64-linux-gnu"
cd "~/GOG Games/The Pillars of the Earth"
./start.sh

As I just ran into the very same issue, on Fedora it is as simple as:
> dnf install libpng12

the package description reads "Old version of libpng, needed to run old binaries". ;)

Copying a "libpng12.so.0" from another game folder into the "game/libs64/" sub-folder of your installation should work as well (successfully tested it with the libpng12.so.0 from a "J.U.L.I.A Among the Stars" installation).

Nevertheless, I'd appreciate if GOG could fix this issue. :)

the link for the package above no longer works. unsure where i can get this package now.??