All the duchies into which Kievan Rus disintegrated were ruled by houses tracing their descent from Rurik. Thus, any one of them could try to "reclaim the ancestral lands" by the standards of that time. Of course, there was a little hitch there since the lands would need "gathering" first...

Moscow ending up the one who actually pulled it off is kinda ironic, though, given that it was very much an upstart that wasn't even there when Kievan Rus was still a polity united under a single ruler. Goes to show just how effective collaborationism (in this case, with the Mongols) can be to build a power base.