To get a little bit of an insight into the single-player, check out theRadBrad on YouTube. He's played a bit of the story around a month ago as well as Shoguki because he was able to play with the developers.
I didn't want to check out the entire videos to not spoiler whatever there may be but what I saw, I'll put into the spoiler tab.
Spoiler: Show
You do get to play each faction and the story is divided into chapters, Not entirely sure if what D_cover said is necessarily true, but it may be. What I am certain of is that you get to fight againts A.I. that very much resembles the one in multiplayer, but it's slightly stronger than your regular little soldiers. Also, you can to a certain extend customize your hero in single-player just as in multiplayer. Didn't dare watch anything of the actual story though.