To be honest, I feel like people do way too much work analyzing why League is such a massively popular game. They talk about how easy to pick up and accessible it is, when (as you pointed out) it can be extremely confusing for new players who aren't familiar with the genre even after ten or more hours of time in-game. Compared to other similar games it's pretty streamlined, but there's still a huge amount to learn and experience before players can be expected to play reasonably well (hence only allowing players to play ranked after they've reach level 30-- which can take hundreds of games).
Personally, I think it's a little more straightforward than that. Metagame player progression systems weren't so widespread when league was released-- I can't say I'm 100% familiar with games from that time, but the only other popular game that offered that kind of system was CoD4 as far as I know. We all know how compelling those systems are now (for whatever reasons), so that was a big plus.
But what really put it over the top is that mobas are an inherently social game. You're on a game with five people, and you've got to rely on them, communicate with them, etc. Wouldn't you rather play with four other friends instead of four people you've never met before and probably never will again? The genre has an inherent incentive for players to get their friends to play, and since the game isn't *impossible* for new players to grasp (ala dota), it's not like they're likely to be driven away by their first few experiences.
Then, those new players get hooked on the progression system that allows them to unlock new characters (right away, mind you!) and such, they keep coming back later to play different characters as the weekly free champions rotate...
But on top of all that, it's just a fun game. Not too punishing when you lose (usually), and fairly rewarding when you win. It's easy to see your progress as you learn the game and master certain characters/matchups/etc, and the now-healthy professional competitive scene gives higher-level players something to discuss, learn from, and aspire to! Basically, there's something for everyone.
