I remember these going back as far as the Super Nintendo in some locations. There was one that had more than a few of these kiosks available around the time Street Fighter II came out and they would hold tournaments in that location. The manager would give away meals and gift cards to the winners of the tournaments that ran several times each evening and on weekends.
That location was packed when tournaments were going and everyone, I mean everyone, had something McDonald's food related in their hands - from drinks to fries. I am sure they made a killing there due to these events.
Not sure why they stopped it. I mean, just because the Wii was not quite right for this, there were other systems available that could have easily taken Nintendo's place in this regard.