Installed on fresh Ubuntu 16.04 x64 (fresh install of Ubuntu).

Starting the game gives nothing but 2-3 sec icon appearence in dash.

If I start throught terminal, game returns this:
alex@alex-Inspiron-7520:~$ '/home/alex/GOG Games/Trine Enchanted Edition/start.sh'
Running Trine Enchanted Edition
./trine1.sh: 31: ./trine1.sh: ./bin/trine1_linux_launcher_32bit: not found


I checked game folder - all bin files existing,
trine1.sh is in /home/alex/GOG Games/Trine Enchanted Edition/game folder
trine1_linux_launcher_32bit - is in /home/alex/GOG Games/Trine Enchanted Edition/bin.

Can someone help me please?

The game page states that some packages must be installed prior to run.
Have you installed them?

https://www.gog.com/game/trine_enchanted_edition