I have never heard those genres referred to as MOBA's. I would say most people (at least people who play games) would know more or less what a MOBA is/isn't, so IMO its not meaningless.
Right, what I'm saying is, if you go up to a person who isn't familiar with the genre and describe it as "multiplayer online battle arena" that fails to actually describe the gameplay at all to the point where, for all they know, you might be talking about arena shooters or something.
FPS? First person shooter. I have a first person view and I'm shooting things. Third person shooter? Same thing except I'm in a third person view. Real time strategy? I have a strategic view of things, and decisions are made in real time. 4x? Explore, Expand, Exploit, Exterminate. Gives me a pretty good idea of what's going on. RPG, I'll admit, is a little worse than these, probably because it stems from tabletop games where you're actually playing a role. And as it turns out, RPG, of those groups, is probably the most widely varied in gameplay mechanics, because it's a term that has a bunch of different connotations.
MOBA says you're doing battle with other players online in an arena. I'm pretty sure there's a way to do a turn based strategy that fits that description. Yes, the connotations of a genre name are important, but isn't it important to have a name that's got actual description outside of the connotations?
/rant