Hello @random2324, this issue should also be brought to the attention of the game's devs.
Copying the file from the ubuntu12_32 folder didnt really helped here, as I still cant launch the game from pts.
Here is the error message presented while I try running the game from pts:

I uninstalled the game and re-installed it and now it works. Dont know why this is needed. As there was no real response anyway, Im closing this.
Nothing extracted yet.
Dirt Showdown gives an error message in the console:
dlopen failed trying to load:
/home/greg/.local/share/Steam/linux32/libsteam.so
with error:
/home/greg/.local/share/Steam/linux32/libsteam.so: cannot open shared object file: No such file or directory
dlopen failed trying to load:
libsteam.so
with error:
libsteam.so: cannot open shared object file: No such file or directory
The game still starts but I regularly use the phoronix-benchmark-suite and there the game doesnt start and just give an error message pop up (gui) like it couldnt find steam runtime or something (sorry, dont remember exact).
I copied now the libsteam.so from the ubuntu32 folder into the linux32 folder and the message went away. However the game now hangs if you want to quit.
Things were working without any issues one month ago, so it seems there was regression introduced last steam update.
I also tried with steamruntime enabled or disabled but the error was the same.