The ffmpeg.exe that comes pre-loaded with Dolphin Pro is for linux. It may seem like it is for Windows because of the .exe extension, but believe me it won't work with a Windows setup.
You have to swap it out with the Windows ffmpeg version in order for it to work. Fortunately, Boonex provides a Windows build of ffmpeg. You just need to download the file and swap it out.
You can download the windows ffmpeg from boonex on their downloads page here:
Scroll down until you see the "Converter" (ffmpeg) button and click on it to download it.
Once you download and extract it you have to replace the current linux ffmpeg located:
With the file you just downloaded from Boonex. Just delete or rename the current ffmpeg.exe and upload the new file to the same location.
After doing so you can check your administration panel -> Tools -> Host Tools
Scroll down to the ffmpeg output selection and you should see something like this:
Now try uploading / re-encoding a video to see if this works on your Windows server / Windows hosting account.