The actual innovation in Dota 2 was on the esports side. From setting up the $1 million International before the game was even released spawned an industry of professional players, sponsors, casters, personalities and production companies. The competitive Dota scene before Dota 2 came out was tiny in comparison.
Twitch was central to this as well, bigger tournaments meant increased viewers, increased viewers meant that Twitch could in turn sponsor even more tournaments.
Maybe I'm wrong, but isn't league of legends more responsible for building the robust esports scene for moba's? It was already there when DotA2 came around, wasn't it?
League's first championship was held in June 2011 with a prize pool of $100,000 [1], and the first Dota 2 International was held in August 2011 with a prize pool of $1,600,000 [2]. Not that big of a time difference, and the difference in prize pools has only increased since then in favor of Dota 2.
Twitch was in baby shoes back in 2011 as well. Game streaming overall was still really small, and sites like own3d.tv held a large market share back then.
In addition, Valve built in-engine spectating into the game since day 1. You can watch other games live, or download replays and jump to any moment in time. League doesn't have similar tech even in 2016 [3], they are definitely far more focused on their casual players. League does have an extremely large playerbase in total, so their esports achievements are still remarkable due to sheer scale, but it's much more of a side-part of League than Dota.
[3] From what I understand there is no replay system at all, and the League spectator mode is very basic and lacks most of the features that Dota 2 has.
Per point #3, it's even gotten as far as becoming a meme in the League community. It's one of the most talked about missing features other than a sandbox mode, which Dota also has.
Any time a new feature is released, especially smaller ones, there's usually a good number of 'We got this but no <replay|sandbox> mode' comments.
Twitch was central to this as well, bigger tournaments meant increased viewers, increased viewers meant that Twitch could in turn sponsor even more tournaments.