How to create an application with applescript that will be able to open a file from finder
Using the argv parameter with the run handler is designed for arguments passed to the script when using it with osascript from the command line.  In a regular AppleScript application, an open handler is passed a list of aliases (HFS paths), for example:

on open fileItems
    repeat with anItem in fileItems
        # do something with anItem
    end repeat
end open


From your snippet, you would do something like:

on open fileItems
    do shell script "/usr/local/bin/zathura " &amp; quoted form of POSIX path of item 1 of fileItems
end open


Note that you should use the POSIX path of items when using them with the shell, and the paths should also be quoted or have characters special to the shell escaped.

See the AppleScript Language Guide for more information.