So, judging from the results, this was an individual tournament?

I've yet to properly try out Washizu mahjong against people (I have the Akagi game for the Nintendo DS), but my impression is that teams add quite a lot to the strategy of it, and I feel that playing it with four individuals rather than two teams would mean that people would rarely win except for by tsumo. With teams things can work a bit differently.

I have watched Akagi recently and to me it seemed the rules for playing in a team format seemed simple enough. You can consider it a 'two-headed dragon' kind of system, only with one head being bigger than the other.

In Akagi, basically the only points that matter in the team game during the whole Washizu arc, are those of Akagi himself and Washizu.
Their partners are seated to their right.
While the partners earn points on their own with their wins as per normal rules and gameplay, at the end of a game session, either Akagi or Washizu has won based on their point total.
For example, they could play the entire session stealing only points from their partner, but if Washizu would end up in third place and Akagi in fourth, Washizu would've still won because he ranked higher than Akagi.

Well, generally speaking, the 'main players' will never end up in the third and fourth place as their partners are supposed to make sure that the main players get as much points as possible...Though, I suppose in real life it is actually possible that they'd end up in third or fourth place together.

The way I see it, in order to play in teams, you determine which person in the team will be the lead and thus accumulates all the points and the other will be the partner, whose main purpose is to play a supportive role by trying to "steal away" the opponent's dealer turns, play into the lead's hands and the deplete the points of the lead of the opposing team. Naturally, if a 'supporter' wins on a self-draw, his partner will have to pay points as well, so unless it's really convenient, supporters generally won't go out on a self-draw =)

One specific rule, however, that should be added in a team format in my opinion, is the "Head Bump" rule from traditional Japanese mahjong.
What this entails is that when two players are in Tenpai and one of the other players discard the winning tile, the person on the right of the player who deals the tile wins.
Following the Akagi example, if Washizu and Akagi are in tenpai and can go out on the same tile, when Washizu's support discards the tile, Akagi wins because he's seated to the right of Washizu's support. I think this rule will add a whole different level of strategy to the team format and makes 'dealing into the lead's hands' a whole lot riskier if the other team's lead is in tenpai as well.