DotA, League of Legends, and similar games are often misclassified as Action Real Time Strategy (ARTS) games. ARTS implies a sub-genre of RTS, but these games are not RTS games and therefore not a sub-genre of RTS. They should not be classified as Action RTS games.
To be considered part of the RTS genre a game must have these 5 features.
In RTS games worker units gather resources by mining them or constructing buildings in key locations to gather them. In DotA players get gold for killing enemies. This is nothing like gathering resources in RTS games. It is very similar to RPGs where players loot slain enemies for gold.
There is no base building in DotA.
There isn't any real technological development in DotA. Players can level up their characters and get new items and abilities, but this is exactly what is seen in RPG games.
Typically a player only controls a single unit in DotA and it is controlled more like it is controlled in RPG games such as Diablo.
This is the only feature out of the five that DotA actually has, but so do millions of other games and other genres such as First Person Shooters. To be considered an RTS a game has to have all 5 features.
Some people argue that because Defense of the Ancients (DotA) is a custom game modification for WarCraft 3 (WC3) that it somehow makes DotA an RTS or part of a sub-genre of RTS. This would be true if it actually used the RTS gameplay elements from WC3, but it does not. Just like how there are Chess, Poker, and many other custom game modifications for WC3 that don't. Chess and Poker are not an RTS games and do not belong in a sub-genre of RTS just like DotA does not belong in a sub-genre of RTS.
It is also worth nothing WC3 is actually an RTS/RPG hybrid. A distinguishing feature in WC3 is that heroes acquire experience and items, and level up just like in traditional RPG games. The DotA custom game in WC3 uses the hero RPG elements from WC3 and does not use any of the RTS elements from WC3.
There is strategy to pretty much every game ever made and any game that isn't turn based is played in real time. This would be like classifying Quake, Counter-Strike, Grand Theft Auto, and millions of other games under the RTS genre. It would defeat the purpose of having the genre.
Since Real Time Strategy is already a well established and defined genre calling something Action Real Time Strategy implies that it is a sub-genre of Real Time Strategy. If the RTS genre didn't already exist it would be okay to make a new genre called ARTS that fits the description of games like DotA, but since RTS is already a defined genre any name that implies it is a sub-genre needs to actually be a sub-genre of the already existing RTS definition. Using ARTS as a genre for DotA is as silly as using a genre for Doom called Shooting Role Playing Game (SRPG) because players play the role of a space marine and shoot things. If someone had never played Doom they would assume the game is an RPG game with shooting in it.