Well, lines 1-6 are one huge command that create the GUI dialog and assigns the choice you made to the $action variable. The exit code is assigned to $ret (if you click cancel it'll be 1).
The case ... esac block basically defines which command will be executed depending on the value stored in $action. Then eval exec $cmd executes the chosen command (stored in $cmd). This is also redundant, could execute right from the case construct.
[[ $ret -eq 1 ]] && exit 0 # stop execution and exit if "$ret" equals "1"
if [[ $ret -eq 1 ]]; then # double brackets are redundant, I'd use [ "$ret" -eq "1" ] instead
vlc ~/Music/Tutturuu~.mp3 # this will never be executed, guess why ;)