I don't even know why I'm interested in this: I have neither the time nor the desire for games any more. The only game I play is DOTA2, and I want to quit it.
The learning curve is very steep. I'm still learning how to play it after 1+ years with it. For me, the big deal is that it is a new genre (for me) and I also love that it forces teamwork and strategy with players that play a 'support' role which their sole goal is to help a 'carry' win his lane. Check out highlights of Dendi from Navi in Dota 2 International 2013.
I agree with winslow that the main initial attraction is the novelty of the genre. I got into League of Legends a few years ago before DOTA2 was announced, and I find that it's a bit more beginner-friendly and balanced than DOTA. (DOTA fan counter-point: League of Legends is overly simplistic and pay-to-play.)
Coincidentally, the League of Legends world championship final is occurring tonight. Anything you learn about the genre or strategy will apply somewhat to any game in the MOBA (multiplayer online battle arena) genre, so check it out if you're interested in learning more. Riot Games has hired an entire team of casters and analysts, and I find the commentary to be mostly insightful and enjoyable compared to American sportscasters.
To bring this on-topic: I wonder whether Valve will allow non-Steam games to run on SteamOS. League of Legends is directly competitive with Valve's own DOTA2, but Valve has historically allowed you to use Steam purely as a launcher. My biggest fear is that this is yet another walled garden, just one that has embraced its digital nature sooner and better.
As long as it runs on Linux, it will probably run on SteamOS. The question is "would valve block LoL from Steam", and I can't see them doing that just because they have a competing game in that genre.
Steam lets me add non-Steam games to their launcher right now on Windows. Imagine the ribbing they would get from the hypocrisy of making a walled garden on Linux.
The bigger limiting factor would be "games that run on Linux." Does League of Legends play on Linux?
Well, that's just a launcher thing. Given that the OS will be open, I am pretty sure you'll be able to install it. The question is, will it be available on Steam the platform? I can't see why Valve would block it.