Open a terminal and cd into the directory where you downloaded the .zip file, something like:
$ cd ~/Downloads
Extract the .zip file using a program like 7z (make sure to install it using your package manager if not already installed). Command should look like:
$ 7z x HeavenStudioLinux.zip
This will create a .tar file. Extract that file also using 7z:
$ 7z x *.tar
This creates a directory called 'build'. cd into there and into the subdirectory. There you'll find a file called 'Heaven Studio' (use `ls` to check). Make this file executable like so:
$ chmod +x Heaven\ Studio
And finally run the program:
$ ./Heaven\ Studio