When you run start.sh from terminal this is what I get:

karuros@karuros-desktop:~/GOG Games/ION Fury$ ./start.sh
Running ION Fury
./fury_nodrm.bin: error while loading shared libraries: libSDL2_mixer-2.0.so.0: cannot open shared object file: No such file or directory

open up Synaptic package manager and search for libSDL2

install libSDL2_mixer-2.0-0 from synaptic package manager

run the game again and it now works.

if you are still missing any other libraries just look them up in the synaptic package manager and install them and the game will run,