The game leading the way in this respect, is Crytek Kiev's Warface, which is a free to play shooter title that looks - to the layman at least - just like any of the big FPS offerings from Activision or DICE and has the same sort of game play modes, similar weaponry, similar tactics - in short, it's all very familiar.
Except there's more of a competitive edge. There's a new slide mechanic that will take skill to master. There's visual unlocks for those that are the best on the server at the end of the day - promoting skilled play through rewards - and varied classes that encourage specialisation.
However it won't just appeal to pro players and experienced FPS gamers, since Warface is free to play. Just like League of Legends, you can play one hour of fifty and you won't have to pay anything. However if you want a quicker respawn in the offline (PvE) mode, or fancy some visual tweaks for your character, that'll cost you a few dollars.
Think it will work? Think it won't? Regardless, it already is. In Russia, where its been available since April last year, there's already five million players. You can join the beta now if you're in the NA or EU regions, with the full game expected to be available where you are later this year.