I tried that...and when I tried running it from within the terminal I got -
dvdstyler: error while loading shared libraries: libavcodec.so.52: cannot open shared object file: No such file or directory
It's another one from ffmpeg. I had these same issues:
root:# locate libavcodec.so
root:# cd /usr/lib/
root:# ls -l libavcodec*
lrwxrwxrwx 1 root root 31 Sep 2 18:57 libavcodec-cinelerra.so.51 -> libavcodec-cinelerra.so.51.57.0*
-rwxr-xr-x 1 root root 3404588 May 23 03:19 libavcodec-cinelerra.so.51.57.0*
-rw-r--r-- 1 root root 8495100 Jul 4 00:49 libavcodec.a
lrwxrwxrwx 1 root root 23 Aug 9 13:58 libavcodec.so.53 -> libavcodec.so.53.60.100*
-rwxr-xr-x 1 root root 10825496 Jul 4 00:49 libavcodec.so.53.60.100*
In my computer, there is the actual file "libavcodec.so.53.60.100", and there is the link to this actual file named "libavcodec.so.53" (this being the name of the link, which links to the actual file of "libavcodec.so.53.60.100".) This is because I received an error similar to what you received about a file not being found (in my case it was libavcodec.so.53 not being found.) I also had similar errors with cinelerra when I installed it, but I likewise solved these by creating links (note the "libavcodec-cinelerra" link above). I had to do this for various programs, I believe due to some issue with ffmpeg. Anyway, I did get both cinelerra and dvdstyler working, and I'm sure you could get dvdstyler working as well.
So, when you see errors about missing lib-files, just look for a similarly named one (by checking ffmpeg in Gslapt in the "files" tab) and create a link to it (giving the link the name of the file that was reported as missing.) For instance, as was done with libavformat, do the same with libavcodec (and any other reported lib file errors). There's might be about eight of them you'll need to do, and then dvdstyler should work.
ln -s /usr/lib/libavcodec.so.53.60.100 /usr/lib/libavcodec.so.52
and for the rest...
ln -s TARGET LINK_NAME
Note: the LINK_NAME will be the named file that was reported as "No such file or directory" in any error report you get while installing dvdstyler, whereas the TARGET will be the existing file with a similar name to the reported missing file.