MOBA is just something they made up so they didn't have to say 'LoL is similar to AoS'.
... except it's not that LoL is similar to AoS (though it is), it's that LoL is
an AoS map. Which... they're not difficult to describe. Two+ sides, computer controlled smaller critters, player controlled bigger/more important critters, everyone trying to kill everyone else. That's basically it. They're... not hard to identify. At all. Battleships, DotA, the varying AoS-style maps... line wars is arguably a variant, but it's sufficiently differentiated to be its own thing. Mainly by the players controlling spawns more directly -- AoS maps can have that, too (See Tides of Blood, EotA, many others), but it's usually an extra degree off and not tied directly to income.
Really, the problem with moba is they're trying to make a catchall term for something that is a very specific derivative of a very specific style and it's... catching considerably more than that style. Unsurprisingly.
AoS as a term for the style (subgenre, whatever you want to call it) worked for largely the same reason roguelike works, in largely the same way. Fairly descriptive in major strokes of (one of) the defining works within the style. DotA, LoL, HoN -- even awesomenauts -- are AoS-style games because that's exactly what they are, and trying to fit them into some other term starts catching other stuff. Like Arena-style maps (See... what was it, Bloodlines Champions?), which are,
again, just a bloody WC3 custom map.
Could alternately just call them WC3 custom maps and be honest about it, too
Or RTT (Real-time tactical, which is more or less what most AoS games are -- a smaller, more focused RTS with most of the S automated), which would be fine until someone actually pulls their head from their nethers and makes an AoS that takes advantage of modern computers (well, and code less shitty than WC3's) and actual working brain cells. Which I'm
still waiting for *grumble grumble*