Smells like blind hatred of a pretty decent company. The comparison to Sirlin certainly isn't valid.
OK... and how is ARTS more descriptive?
A(ction) -- this says even less than "Battle".
R(eal)-T(ime) -- OK, but lots of multiplayer games happen in real time.
S(trategy) -- again, most games have strategy.
If MOBA applies better to fighting games or FPS games, ARTS applies to them just as much if not more.
If you break it into its roots, it seems even less appropriate. Action RTS? Traditional RTS games already have action. Lots of action. And games like DotA don't make me think of traditional RTS games at all.
And seriously, RTS itself is such a non-descriptive name. You could apply to all sorts of things. At face-value, you could apply it to Galaxy Trucker, or Blitz Chess, or American Football. Why not complain about the prevalent use of RTS as a genre name? Moreover, why advocate using it as part of the name for a very different genre?
I also think that MOBA is perfectly functional as a description of the genre.
M(ultiplayer) -- tells us off the bat that there are almost always more than 2 players involved. Sure, "multi" just means more than one, but in practice it tends to be used for games involving 3+.
O(nline) -- You said that it's not necessarily true, but being "online" just means that the computer is part of a network. That's true even on LAN. Moreover, I'd expect that playing over the internet is significantly more common than playing over LAN. And this is supposed to be a name for a genre, not just DOTA.
B(attle) -- Not every computer game is about battle. Off the top of my head -- Portal, The Sims, Sim City, Rollercoaster Tycoon, Journey, Minecraft (for the most part), Myst, Pong, Oregon Trail, World of Goo, The Stanley Parable, Antichamber, various sports and racing games... Saying "Battle" implies a more direct kind of conflict, and the word suggests something bigger than what you see in the usual 1v1 matchups of the fighting game genre.
A(rena) -- The definition is "a field of conflict", not necessarily a small one. Sports arenas are pretty big, and that's a lot like what I see in MOBA games. Is it a perfect descriptor? Maybe not, but it serves to distinguish it from the bigger scale of RTS games and the sprawling worlds of MMORPGs.