At the moment, it is not possible to 'scrobble' tracks from an Internet radio stream with Rhythmbox.
When this question was posed as a bug report/feature request here: https://bugzilla.gnome.org/show_bug.cgi?id=376659 it was marked by the Rhythmbox developers as being something that won't be fixed due to the nature of Internet radio streams not providing the correct metadata to be able to determine the correct artist and title.
If a user is playing a stream instead of a regular file, do not submit that stream/song.
Do not try to guess info from the filename - if there are no tags, don't submit the file.
The shoutcast metadata provided by most streams only includes a single
title string which cannot reliably be split into artist and song title