For me, I'd like an "easy to learn, hard to master" game that's enjoyable to watch.
The first one is mainly because if esports wants to grow, they sooner or later have to draw in people who don't play the game themselves. Heck...non-gamers, even. If it's not watchable and directly understandable who's winning and who isn't, something is wrong.
The second part is a bit harder to explain. Watching someone play is a different experience than actually playing the game, so the fun is different. Add into that that it's a multiplayer game where different players duke it out. That makes it harder to keep an overview of how the general match is going. For this, most gametypes are immediately dropped (I have no doubt FPS'es are incredibly fun to play and hard as hell...but watching them is a chore).
Personally, I prefer RTS'es. There's something simple about "the first team to lose their base loses". And with a spectator seeing both sides and some good commentators, it's easy to follow the match even if you haven't played the game yourself (I got my girlfriend watching starcraft 2 with me at some point).
And for the love of god:
no fighting games. Yes, I KNOW. It's ABSOFRICKIN' INSANE in kind of tactics, quick button presses and reacting to what your opponents do. Congratulations to you, but...it doesn't show. I mean...
look at this. I really don't want to bash these players or the ones liking it...but it's not for me. It really isn't. All I see is some characters spasming back- and forward...and an audience that goes wild over it for some reason.
(honestly...I feel like uploading a youtube-video: me and my little brother - both equally unskilled in street fighter <insert number> - just button mashing away and not hitting each other...and an audience that goes wild when at the final seconds one of us DOES hit the other. I really wouldn't be able to tell the difference between that and what these world class players pull off)
Blizzard's new MOBA: Heroes of the storm, their very own "Smash bros" is a prime example of the expanding market.
Even the mafia of the gaming world EA are looking to start cashing in on the eSports scene.
For the record...you DO know that blizzard and EA can't be pretty much further apart in terms of game development, right? Blizzard tweaks and supports their games sometimes years after release. On EA's end, they...don't. For this reason, I think a random indie developer has a better shot at creating a game that'll dominate esports one day.