You're thinking of the "Real-time tactics" genre, which is a sub-genre of real-time strategy. While these points you've listed to help define real-time strategy games, they aren't only exclusive to that genre.
In order for a game to qualify as a real-time strategy game, it must progress in real-time, as opposed to turn-based strategies like the franchise "Civilization", and have gameplay that revolves around strategic thinking and have a set goal to fulfill.
If League of Legends' gameplay progresses through real-time and revolves around strategic thinking and planning, it's a real-time strategy. This also goes for MOBAs, too.
Hey if were going to argue with that kind of logic then Quake 3 should be a MOBA too. It is real time and takes place in an arena. I know people in the league community that don't consider League an RTS. It is just in it's own genre, MOBA.
The RTS Genre is composed of these elements:
Real Time
Base Building
Full control of all Units
Resource Gathering
Diverse Maps
A game like SimCity could be called an rts because you are building a city, things happen in real time, you are full control of the city by creating laws and deciding where to build your structures, and you are gathering resources by creating taxes.
What does league have:
Things happen in real time
You have control of a single hero
Minions are controlled by an AI
There is not base building
The only form of resource gathering is through bounties collected by killing minions and other champions
Arena
Leveling Up
Remove the base building aspect from the RTS and focus more on the unit aspect and you have what is called the Real Time Tactics genre.
However since League lacks all of the elements of an RPG and RTS it is called a MOBA(Multiplayer Online Battle Arena). The term Action RTS is rarely used, but refers to the fact that you using RTS controls to move around and attack with a single guy rather than multiple units.
The game Natural Selection could be called an RTS. IT is a shooter, but both teams have a commander who place down structures and power-up items to help out his team, his team mates have to co-operate with the commander by working together to build his structures and attack where told to. The players will perform all the building and attacking, the commander places structures and researches upgrades for his men.
