I'm pretty sure Karkat explained the flow of the game to John at some point. I can't be arsed to find the relevant logs, but it wasn't too complicated.
Black and White are locked in an eternal stalemate in the timeless expanse of the Incipisphere. When a player enters the Medium, his kernesprite hatches and the chess metaphor game becomes more complex as the battlefield expands and the quasiroyals assume the prototypings. This throws the game off balance, giving one side a chance to win. Now, in a normal game, this is inevitably black, who is destined to get win the war, get the white scepter and start the reckoning. At this time, Skaia activates its defense portals, and the players have for however long they last to kill the black king, at which point Skaia is saved. The denizens each guard a huge grist hoard that will be used for something called "the ultimate alchemy", and it's not exactly clear yet how this ties to the rest of the game.
Also, the game doesn't "reset", as far as we know. If black wins, what you get is a null game session with dead players, crushed Skaia, and presumably Derse reigning over the medium for all eternity.
What's supposed to happen when you win the game is also a bit of a mystery. The stated goal is saving Skaia, the source of all creative potential in the universe. Whether or not this actually means something has yet to be seen. The trolls won their game, but something apparently happened and now they're doomed for some reason.
I have a really cool theory about the real purpose of Sburb, which I posted earlier, and am now going to post again because it's so cool.
The trollflash really illustrates how dysfunctional trolls are, as lampshaded by Kanaya's thoughts on Rose's walkthrough. They have a lot really tangled and conflicting romance going on, along with plenty of old vendettas and a general tendency to respond to things not going well by crushing their enemies. The humans, by contrast, are best friends. And that's it. They make an excellent team and would never try to backstab each other.
This could also be what Terezi meant when she said they were all crazy in their own way. All the trolls have some glaring personality flaw that makes it difficult for them to work as a team with most of the other trolls. The game will be mostly about them learning the true meaning of friendship. The humans already know all about that, and their psychological problems are mostly focused inwards. Sburb will force them to confront all their insecurities and delusions to realize the elaborate roles the game has generated for them.
Which got me thinking: Maybe that's what it's for?
IDE/THEORY: The true purpose of Sburb is to facilitate the emotional growth of a small group of thirteen-year-olds. Their home planet is collateral damage, and the game takes some measures to repair it by sending the exiles to restart civilization. Also, the reason the troll game appears ruined is that they haven't quite achieved that yet. Killing the black king was largely pointless in the big picture, and the game is still going on. During their 600-hour-long campaign they learned the value of teamwork, but their response to an outside problem is still to troll some strangers backwards in time and try to get them killed and things like that. They will only win when they work together with the humans.
I think something like this can be found under the hood of a lot of games. Especially JRPGs. The world is ending in fire and meteors, but this isn't really what the game is about. The armageddon is just something that forces the main characters to overcome their psychological problems. And though they made a lot of progress, the trolls failed to discover the True Meaning of Friendship, so now the game is improvising and ending their world again. It probably orchestrated the summoning of Lord English to eat the universe just to force them to cooperate with new people.