>>413
It's just a .tar.bz2 archive with the executables inside, similar to a .zip. You can probably right-click > Extract... or something in a fancy GUI, but this is how to do it using the command line:
tar xjf katawa_shoujo_blahblahblah.tar.bz2
cd Katawa_Shoujo_blahblahblah
./Katawa_Shoujo.sh
You may need to chmod +x Katawa_Shoujo.sh
before that last step to make it executable. Then you're good to go.