Comment 10 for bug 185928

I noticed the same behavior in Totem. I found a related Gnome bug that explains this behavior:
https://bugzilla.gnome.org/show_bug.cgi?id=370732

Space is reserved to activating widgets for accessibility purposes. It can't be used for anything else. There's an entry in the Totem FAQ about this:
http://projects.gnome.org/totem/#faq

You can make Space toggle playback right now by first highlighting the Play button in the toolbar by pressing Tab.

The behavior you're seeing during playback - the song starting from the beginning - is cause by the action associated with the song list widget, which is normally the selected widget. The behavior of the song list widget could be changed to toggle playback. Or keyboard focus could switch to the play button automatically after you start a song, though I don't think that's a good idea.