You need to post your router settings ... I can't help without this.
Also, if the tool works in your local network then the tool just works ! The issue accessing the tool from outside (public) is related to the router not set up properly or just not doing what it is expected to do.
Post some screenshots from the Enigma-TV settings ans alos from your router.
As yo said this is a router issue. By looking at your pictures, I would have made the same settings myself ... But this router options looks strange as you cannot specify the public vs the local ports. The best is to ask your provider on how to redirect port on their router model.
i've been using this program for some time now and it was working great.
Now i moved to another home with a different laptop and i cant get the public stream to open on vlc. I'm using the same ports only the router is different. At my other place i had a linksys router and now the internet provider has their own routers , but i can adjust ports via their website.
The internal stream open perfectly , its just the public one ...