That is not how it works. for a game to be a subgenre of RTS it would itself have to be an RTS and the subgenre would just be more specific. Like say Left 4 Dead is an FPS, but its also suggenres like survival game, horror game, zombie shooter. All of those subgenres without stopping it from being an FPS.

But Tower Defense games also just started out as a mod for an RTS game. That does not make Tower Defense games RTS games. Many mods in Warcraft 3 were RPGs, without being RTS.

RTS games should have some kind of resource gathering element, something deciding what units to get during the game, to form a strategy. In DotA you can have strategies of how to play, but you can have that in FPS games as well like Counter Strike. They are still tactical games though, because strategic decisions is stuff like "what buildings will I need for my strategy", "how many of each unit makes for a good combination", "the enemy now has air, should I counter by trying to stop him from making more air units, or do I have to do more to counter air units"?

So MOBA is not RTS.

By your definition, MOBA is not RTS.
But RTS is not only limited in Dune II/C&C/Starcraft gameplay style.

The Ancient Art of War, Populous, Powermonger also are RTS, but by your definition? Maybe they are not RTS.

By my definition they are. Resources in Populous is your population and mana, you have to plan what powers to use and where. So much more strategic than tactical. The methods of making units is just different from other RTS games. Powermonger I am not sure about since I have not played it. I know I should have, but I just missed it back when my Amiga was my main computer. The Ancient Art of War? That sounds very strategic.

Whether MOBA is an RTS has been debated several times. I would think the RTS argument never won.