Yes, mobile in this context is very different. Or rather, local is very different. Building a database that resides on a local device and is primarily accessed by a single user is an entirely different class of problem than one that is on a server. Usually most of the hard problems in building a database system involves dealing with multiple people accessing or modifying data at the same time. When you have a single user, that problem either disappears or is massively reduced.
As you said, Realm does appear to have a server offering now, but from the sounds of it, it hasn't really been proven yet, so I don't think it's as easy as saying they've succeeded where Rethink failed.